Why don't negative square roots exist?

It is true that square root of a negative number doesn't exists. Because square root of a negative number is a complex number. √-1= imaginary number( i )

Hi Leia, √ - n can exist if you think imaginatively. Use numbers as imaginatively as Einstein and Hawkings do... Formulaic terms don't always cut it. I guess you are F rather than M right!? My example: A farmer has an orchard where each tree bears twenty apples every year (x), year on year. Yield per tree over time = 20x Suddenly one tree bears no apples in one year Yield The total yield over years is therefore 20x - 20 The tree dies before the next harvest. The total yield year on year is now 20x -20˙ In real life terms the farmer has lost one tree and it's yield year over year. This can be expressed as 20x - 20˙ or in terms of trees simply: -1, but not quite: taking into account the impact of the lost tree, we might express it as √ -1, this being the "radical" of the lost tree. The alternative expression to 20x - 20˙ is 20x - (√ -1) I urge you to think of numbers imaginatively! I hope this makes it more fun and bends your mind Pete x

What you’re saying is 20x-(root(-1))=20x-20 which Is false.

You didn’t introduce exponents anywhere

Square root of a negative number does not exist because square is either positive or zero. Yes, square root of a negative exist not in real numbers but in complex number. Square root of a negative is iota which can't be plotted on real number line but we can plot it in imaginary axis that is vertical axis of acomplex plane

The answer to this question is that negative square roots don't exist because they can't be represented in the form of a real number. Negative square roots are represented by the letter i, which represents the square root of minus one.

As we know that square of any number(positive or negative) gives always a positive answer. In case of root solving, root of a negative number terminates into a Greek letter iota(i) i=√-1 i²=-1 If we have an algebraic equation x²=-1 Then taking root on both sides gives x=√-1 or x=(i) iota

You already have a lot of good answers but more importantly we can use the square root of -1 (i) as a modelling tool which makes calculations easier. This is a subject called complex numbers and they are used extensively in physics especially quantum mechanics. They also appear in Euler's equation - look that up

Negative square roots do exist in the context of complex numbers, but they do not exist as real numbers. The square root of a non-negative real number x is a number that, when squared, gives x. For example, the square root of 4 is 2, because 2 squared is 4. However, if x is negative, then there is no real number that can be squared to give x, because the square of any real number is always non-negative. For example, there is no real number that can be squared to give -4, because the square of any real number is always positive or zero.

Negative roots do exists but they are not real numbers.Thesquare of a positive or negative number is always positive,so there is no a real number that has a negative square.Therefore the square root of a negative number is not a real number.

Negative square roots do exist in the context of complex numbers, but they do not exist as real numbers. The square root of a non-negative real number x is a number that, when squared, gives x. For example, the square root of 4 is 2, because 2 squared is 4. However, if x is negative, then there is no real number that can be squared to give x, because the square of any real number is always non-negative. For example, there is no real number that can be squared to give -4, because the square of any real number is always positive or zero.

Negative square roots do not exist in the set of real numbers, but they do exist in the set of complex numbers. A real number is a number that can be represented on a number line. Real numbers can be positive, negative, or zero. Complex numbers are numbers that can be represented as a sum of a real number and an imaginary number. Imaginary numbers are numbers that cannot be represented on a number line. The square root of a number is a number that, when multiplied by itself, equals the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. The square root of a negative number does not exist in the set of real numbers. This is because no real number, when multiplied by itself, equals a negative number. However, the square root of a negative number does exist in the set of complex numbers. The square root of -1 is called the imaginary unit and is denoted by the letter i. The imaginary unit is not a real number, but it is a complex number. The square root of any negative number can be expressed as a product of the imaginary unit and a real number. For example, the square root of -4 is 2i, because (2i) x (2i) = -4. Negative square roots are used in many different areas of mathematics, physics, and engineering. They are also used in many different applications, such as signal processing, control systems, and cryptography.

Yes they do not exit under real numbers domain. But, can be solved if we expand the domain to complex numbers

Negative square root does not exist

Negative numbers doesn't have real square roots since a square is either positive or 0. If the radicand is not a perfect square i.e. the square root is not a whole number than you have to approximate the square root (unless we can keep √3 as an answer).

Because no number times itself can equal a negative number.

Yes, it's simple and true answer. There is no number whic multiplying itself gives the negative number.

Because it’ show’s imaginary line

a square is either positive or 0. Negative numbers doesn't have real square root.

Integers can be expressed as Negative or Positive. Real number is any number from 0...n. When we mathematics is being used to solves advanced and complex solutions, the solution do sometimes have a negative component, which gives an explanation of another understanding or and identified phenomenon that existed from the solution of problem being studied.

You can have negative square numbers but they are encountered in much higher maths..... they are called imaginary numbers.

Negative numbers don't have real square roots since a square is either positive or 0. If the radicand is not a perfect square i.e. the square root is not a whole number than you have to approximate the square root (unless we can keep √3 as an answer).

They do exist, they’re called imaginary numbers. You’ll probably learn about them in higher grades/levels of your math classes. But for now, just take what your teacher told you and work with it.

Negative square roots do exist in the context of complex numbers, but in the real number system, negative square roots are not considered to be valid. The reason for this has to do with the definition of a square root. The square root of a number is defined as the non-negative number that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 multiplied by itself equals 25. However, there is no real number whose square is negative, because the square of any real number is always positive or zero. To see why this is the case, consider the equation x^2 = -1. If x is a real number, then x^2 is always greater than or equal to zero. Therefore, there is no real number that satisfies this equation. However, we can define a new number system called the complex numbers, which includes a number i such that i^2 = -1. In this system, we can take the square root of a negative number by expressing it as a multiple of i. In summary, negative square roots do not exist in the real number system because the square of any real number is always positive or zero. However, negative square roots do exist in the context of complex numbers.

Square roots of negative numbers can be exist but in the form of complex number,

The root of a number is the quantity which when multiplied by itself yields the original number. Negative numbers do not have real roots because when a negative number is multiplied by itself, it yields a positive number, which is the case for a positive actual number. Thus, the inability to yield the original number.

In mathematics, the square root of a non-negative number is defined as a number that, when multiplied by itself, results in the original non-negative number. For example, the square root of 4 is 2, since 2 multiplied by 2 equals 4. However, it is not possible to take the square root of a negative number and obtain a real number, since there is no real number whose square is negative. This is because the square of any real number is always non-negative. To represent the square root of a negative number, mathematicians use the concept of imaginary numbers. An imaginary number is defined as a multiple of the square root of -1, denoted by the symbol "i". For example, the square root of -4 is 2i, since 2i multiplied by itself equals -4. Therefore, negative square roots do exist in mathematics, but they are represented using imaginary numbers.

When using 'ordinary' numbers (technically, the real numbers, i.e. numbers on the usual number line), square roots of negative numbers don't exist. But mathematicians have invented (discovered ?) lots of different number types, for example, complex numbers. Other number types ('number systems') exist too - see Wikipedia. Square roots of negative numbers do exist when using complex numbers. For example, √-2 = i√2. The 'i' is a complex number; it's a symbol for √-1. Complex numbers are normally studied further in secondary school. Complex numbers have uses in many areas of physics and engineering.

This is because to get a square number, you have to multiply the same numbers and their signs must be the same. -2 x 2 = -4 but -2 isn't the same as 2 so -4 isn't a square number. So negative squares don't exist

because negative square roots of 1 is undefined.

The maths teacher is partially correct.There is no real number that is the square root of a negative number. However, we can represent the square roots of negative numbers using imaginary numbers, which are numbers that can be expressed as a real number multiplied by the imaginary unit i, where i is defined as the square root of -1. For example, the square root of -2 can be written as i√2.

Hello, you might have got the answer, but this is because the product of a real number by itself is always positive.

Square roots with negative numbers do exist. They are located on the vertical axis in the complex plane, which is at 90 degrees. For example i = e^i(pi/2) which means that i is a POINT on the unit circle in the complex plane at the angle pi/2 = 90 degrees. All other i's are located on the vertical axis in the complex plane.

Since the definition of a real number is any number whose square is not negative, "imaginary" numbers do exist as numbers whose square is negative and these are multiples of the "imaginary" unit i. Therefore, these numbers do exist as points on the vertical axis in the complex plane (with real and imaginary parts), where "imaginary" does not mean not real existence but not real numbers where real numbers are simply defined as numbers whose square is not negative and "imaginary" numbers are numbers whose square is negative.

Your maths teacher is partly right. Yes! Square roots of negative number does not exist “in the REAL number system”. The real number system has to do with all kinds of numbers we have in the real world. Positive whole numbers, negative whole numbers, fractions, decimals… But the real number system is not the only number system we have in algebra. We also have the COMPLEX number. So in the complex number world, square root of negative numbers do have a solution. A peculiar entity of the complex number is the imaginary number or unit denoted by i. That is not the English letter i but iota which is the 9th letter Greek alphabet. I know It looks like i 😅. i is an imaginary number and the value is square root of -1. That means if I have square root of -4, we can get a solution for it in the complex number system. Square root of -4 is same as square root of 4 multiplied by square root of -1 Square root of 4 is 2 Square root of -1 is i That means square of -4 is 2i That solution is a complex number I hope you understand it now.

Hi Leia. Square roots with negative numbers do not exist. This is because when we are squaring any number, we multiply the number with itself. So 4 multiplied by 4 gives 16 as the square of 4. Now if you square negative numbers, such as -4, you will get -4 times -4, which is again 16. So by squaring a number, it is never possible to get a negative number as the result. This is why positive numbers have square roots, but negative numbers cannot have square roots. I hope that answers your query.

Negative numbers doesn't have a real square root since a square is either positive or 0.

The square root always would positive number or zero. If the square root is negative so it is considered in complex number.

Negative square roots means no existence. A very helping method is herons formula.

Leia, think about it this way: If you take the square root of a number, it means that if you multiply that value by itself, you'll get the square. eg √4 = 2 This means that 2 x 2 = 4 Now, if you multiply a positive number by itself, you'll always get a positive number. eg 2 x 2 = 4 Similarly, if you multiply a negative number by itself, the negatives would cross out and the result would be positive. eg -2 x -2 = 4 For this reason, it is not possible to take the square root of a negative number, because if you multiple any number by itself, whether it is positive or negative, you will always get a positive result. So, you can only take the square root of a positive number and not a negative number. Hope this answered your question. Cheers!

Leia, think about it this way: If you take the square root of a number, it means that if you multiply that value by itself, you'll get the square. eg √4 = 2 This means that 2 x 2 = 4 Now, if you multiply a positive number by itself, you'll always get a positive number. eg 2 x 2 = 4 Similarly, if you multiply a negative number by itself, the negatives would cross out and the result would be positive. eg -2 x -2 = 4 For this reason, it is not possible to take the square root of a negative number, because if you multiple any number by itself, whether it is positive or negative, you will always get a positive result. So, you can only take the square root of a positive number and not a negative number. Hope this answered your question. Cheers!

Leia, think about it this way: If you take the square root of a number, it means that if you multiply that value by itself, you'll get the square. eg √4 = 2 This means that 2 x 2 = 4 Now, if you multiply a positive number by itself, you'll always get a positive number. eg 2 x 2 = 4 Similarly, if you multiply a negative number by itself, the negatives would cross out and the result would be positive. eg -2 x -2 = 4 For this reason, it is not possible to take the square root of a negative number, because if you multiple any number by itself, whether it is positive or negative, you will always get a positive result. So, you can only take the square root of a positive number and not a negative number. Hope this answered your question. Cheers!

indeed!

Mathematically, it won’t be totally correct to say square root of negative numbers Donets exist. For a preliminary stage like high school, it is sufficient for you to know that it doesn’t exist. Why? The simplest way to explain the square root of a number is that If you are seeking to get the square root of x for example, then you are looking a number you can multiply by itself to give you x So the square root of 4 is 2 or -2 because 2 or -2 are the numbers you can multiply by itself to have 4. 2 x 2 =4 -2 x -2 =4 Also, the square root of 36 is 6 or -6 because 6 or -6 are the two numbers you can multiply by itself to have 36 6x6 =36 -6 x -6 =36 Now what is the square root of -16? Is it 4? 4 x 4 =16 -4 x -4 =16 Meaning that in this context, negative numbers don’t have square root. But if you go further in Advanced mathematics, the root of negative numbers forms complex numbers.

Square roots of negative numbers are not real numbers. However, if you extend your definition of "number" from the one-dimensional real line to the two-dimensional complex plane, square roots of negative numbers do exist. sqrt(-2) = i sqrt(2), where i = sqrt(-1).

The negative number does not exist.its complex number.

Square roots exist only for real numbers. Square roots of complex numbers don't exist. As complex number has two parts as the sum of real and complex part. When you take square root then how can you split out square root of real and imaginary part. There is no such a property in numbers.

Negative numbers doesn't have real square roots since a square is either positive or 0. If the radicand is not a perfect square i.e. the square root is not a whole number than you have to approximate the square root

Negative square roots do exist, but they are not real numbers. They are complex numbers. When you take the square root of a negative number, the result is a complex number with an imaginary component. Imaginary numbers are numbers that involve the square root of -1, denoted as 'i'. When you take the square root of a positive number, you get two possible solutions: one positive and one negative. For example, the square root of 9 is both +3 and -3, since 3² = 9 and (-3)² = 9. However, when you try to take the square root of a negative number, like -9, there is no real number that can be squared to obtain a negative result. This is because the square of any real number, whether positive or negative, is always positive or zero. To resolve this issue, mathematicians introduced the concept of imaginary numbers. The square root of -1 is represented by 'i', and the square root of any other negative number can be represented as a multiple of 'i'. So, the square root of -9 can be expressed as 3i, where 3i² = -9. Complex numbers are numbers that have both real and imaginary parts, and they are used to handle negative square roots and other operations that are not possible within the realm of real numbers alone.

square roots do exist, but they are usually expressed in terms of complex numbers. However, in the context of real numbers, the square root of a negative number is undefined because the square of any real number is always positive

square roots do exist, but they are usually expressed in terms of complex numbers. However, in the context of real numbers, the square root of a negative number is undefined because the square of any real number is always positive

1. square root of complex number doesn't exist 2. root 2 x (iota)

Already answered adequately. Just write √-1= i and proceed as normal.

Yes because product of a number with same sign is always positive

Negative square dont exist because we can not plot them in real plane we have to plot them in complex plane known as argand plane

The square-root of a number "x" is a number "y" such that y^2=x. Like square-root of 4 is 2, as 2^2=4, square root of 25 is 5 as 5^2=25 Since, square of any number is always a positive number, so if we have a negative number "d" then there doesn't exists any number "b" such that b^2=d. Which means that the square root of the negative number "d" doesn't exists.

Because it's multiple of 2 same number. And as we know the rule of Mathematics. +Ve Number * +ve Number = +ve Product -ve Number * -ve Number = +ve Product In both cases we will recieve +ve Product Soo, if proper square is +ve number, then no negative square root exist

Although there are negative square roots, their applicability as solutions relies on the particular situation in which they are being evaluated.

Squares are always positive or zero, and the lowest Square root is zero. Hence negative Square root not exists since it is not real

The square root of a number is the repeated factor of this number which is the result of multiplying Two identical numbers having the same value and same sign like: +2 x +2 🟰 +4 or -2 x -2 🟰 +4 in both the result is +4 So the root of +4 is either +2 or -2 Which are the repeated factors that are identical having the same value and same sign And also there is no root of -4 Because -4 is a result of multiplying to different numbers which are +2 and -2 And as said before that the factors should be identical having the same value and same sign There is a positive square root of 4 which is +2 And negative square root of 4 which is -2 And the two square roots of 4 are +2 and -2 When we are asked about root 4 we answer the positive factor But when we are asked specially about the negative root of 4 we answer the negative factor

Negative numbers doesn't have real square roots since a square is either positive or 0. If the radicand( an nth root of a number x is a number r which, when raised to the power n, yields x: {\displaystyle r^{n}=x, } where n is a positive integer, sometimes called the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root) are not a perfect square i.e. the square root is not a whole number than you have to approximate the square root (unless we can keep √3 as an answer). Example; The value of root 4 is equal to exactly 2. But the roots could be positive or negative or we can say there are always two roots for any given number. Hence, root 4 is equal to ±2 or +2 and -2 (positive 2 and negative 2). The square root of negative numbers is called imaginary number denoted as **i**

Negative square roots do exist in mathematics, but they cannot be represented as real numbers. The square root of a negative number is defined as an imaginary number, which is a complex number with a real part of 0. For example, the square root of -1 is represented as "i" (the imaginary unit), since i² = -1. Similarly, the square root of -9 is represented as 3i, since (3i)² = -9. The reason why negative square roots cannot be represented as real numbers is due to the definition of the square root function. The square root of a number is defined as the positive number that, when multiplied by itself, gives the original number. Since a negative number multiplied by a negative number gives a positive result, the square root of a negative number cannot be a real number. However, imaginary numbers and complex numbers (which include both real and imaginary parts) are used extensively in mathematics and physics, and are essential in many fields, including electrical engineering, quantum mechanics, and signal processing.

This is not true. Square roots can be written with an imaginary number. For example, the square root of -16 could be written as 4i. I is the letter for an imaginary number.

Negative square roots do exist, but they are not real numbers. The square root of a negative number is an imaginary number, denoted by the letter “i”. For example, the square root of -9 is 3i, where i is the imaginary unit. The reason why negative square roots are not commonly used in basic arithmetic is that they do not have a real-world meaning. For example, you cannot have a negative length or a negative area. However, in more advanced mathematics and physics, imaginary numbers and negative square roots are used to represent complex phenomena.

Square root of √-2 =√(-1×2)=√-1×√2 √2 exist because it is a real numbers but √-1 does not exist because √-1 = i an imaginary or complex number .So square root of √-2 is not a real number, it is an imaginary or complex number. Hence √-2 does not exist as real number.

Roots of negative square root exist but they are imaginary root but not real roots.. So negative square roots gives two distinct imaginary roots or can be said no real roots

Practically square root of a number is a number that multiplies by itself can give the original number. But theoretically, square root of -1 does exist which in mathematical terms, we use the symbol 'i' to represent. We call the number with 'i' as complex number. This kind of math only appears in high school or university.

A negative number multiplied by another negative number will always be a positive number. A square root is doing this process but backwards. For example, square root of 4 is equals 2, because 2 x 2 = 4. What about square root of -4? That’s impossible because no two numbers multiplied by each other equals -4 AND are the same. It will have to be 2 x -2, which arent the same

This is because all integers (+/-) have their squares as 0 or a positive number. There is no integer whose square is a negative

Negative numbers doesn't have real square roots since a square is either positive or 0. If the radicand is not a perfect square i.e. the square root is not a whole number than you have to approximate the square root

Negative numbers doesn't have real square roots since a square is either positive or 0.

Zero has one square root which is 0. Negative numbers doesn't have real square roots since a square is either positive or 0.

Negative square root exists but they are imaginary numbers.

definition : X^2 = x * x now the square root √ is the opposite of power two, so The answer of your questions is the asking of the opposite ... What is the number that you multiply it by itself to give you a negative number ........ the answer is non ex :( +2 )( +2) =+4 (-2)(-2)= +4 positive ... Always any number that you multiply it by itself will give a positive number even though it is negative one . Now for square root : √4 ( what is the number that you multiply it by itself to give you +4 ...it is +2 ) answer : √4=+2 but √-4 has no answer ( there is no number that can be multiplied by itself gives -4)

definition : X^2 = x * x now the square root √ is the opposite of power two, so The answer of your questions is the asking of the opposite ... What is the number that you multiply it by itself to give you a negative number ........ the answer is non ex :( +2 )( +2) =+4 (-2)(-2)= +4 positive ... Always any number that you multiply it by itself will give a positive number even though it is negative one . Now for square root : √4 ( what is the number that you multiply it by itself to give you +4 ...it is +2 ) answer : √4=+2 but √-4 has no answer ( there is no number that can be multiplied by itself gives -4)

Because a square of negative number is positive as well as the square of positive number. And this is in the real

Because square root of a negative number is a complex number. √-2 can be written as √-1×2 where √-1 is a imaginary number and square root of imaginary number( i ) does not exist. Thanks

Hello student Negative square root doesn't exist because the product of same sign of any number is always positive Example -2 *-2 = +4 2 * 2 = 4

It does exist in imaginary plane.

Simple way is Nagative square roots is −√b and to indicate both roots write ±√b in real time not considering negative.

Because in Real line (R) only real number exist. and √-2=2i which is not exist in R .because 2i is imaginary number.

the value of squarerroot of -2will be squareroot 2i. where i is the imaginary value i-squareroot of -1

A negative number such as -2 is a real number but there's no real number solution to the square root of a negative number. The square root of number is that number which if multiplied by itself give you the original number. Square root of 4 is 2 (because 2 x 2 =4). But square root of -4 = (square root of (-1)) x (square root of 4) = 2x(square root of -1); the square root of the negative number is not known so it's represented as "i" (imaginary)...

Negative square roots do exist, but they are not defined as real numbers. The square root of a non-negative number is defined as a non-negative number. For example, the square root of 4 is 2 because 2 x 2 = 4. However, the square root of a negative number is not defined as a real number because there is no real number that, when multiplied by itself, gives a negative number. To represent square roots of negative numbers, mathematicians use the imaginary unit i, which is defined as the square root of -1. Any complex number of the form a + bi, where a and b are real numbers, is called a complex number, and i is the imaginary part of the number. For example, the square root of -4 is 2i, because (2i) x (2i) = -4. Similarly, the square root of -9 is 3i, because (3i) x (3i) = -9.

Yes, the Maths teacher finds it easier to tell pupils this way in elementary Maths that the square roots with negative numbers do not exist because of the level of understanding of the pupils at that level. However, it is also easier for students to grasp the concept better as they advance their understanding of numbers from real to complex numbers at higher level. They will be aware that √-2 can be written as √-1 * √2, where √-1 = i, or i^2 = -1. That way, it can now be practically understood that √-2 = √2*i, and √-4 = 2i, etc, in complex number parlance, where we have real (a) and imaginary (bi) parts with “i” (i.e., z = a + bi). Hence, the concept of complex number helps us to appreciate that square roots with negative numbers do indeed exist.

you will always get an error, as you can not square root a -ve number.

Yes. Because it becomes complex numbers. Your calculator only deals with real numbers. So that's why it can not answer you.

Square roots of negative numbers do exist and play a role in solving engineering problems, physics problems and elsewhere. The square root of any negative number does not exist in the real number system, but in the complex number system. Complex numbers are expressed in the form a +bi, where i equals the square root of negative one. If i is the square root of negative one, then i squared = -1. This allow us to represent numbers such as the square root of -49 as the square root of (-1)*49 which is equivalent to i*square root of 49 , or 7i. Complex numbers allow us to represent solutions in a more generalized way. We first probably encountered complex numbers using the quadratic formula to solve a quadratic equation. Somes the discriminant. b^2-4ac, is negative, which implies that there are no real solutions to the quadratic equation, but the solutions are complex. The graph of a quadratic equation, or quadratic function, is a parabola. The solutions to the quadratic equation are equivalent to the x intercepts of te graph of a parabola. When the disscriminant is negative, the solutions do not exist in the real number system. This means the graph of the parabola does not touch the x axis. For more applications of complex numbers, look up De-Moivre's theorem on roots and powers of complex numbers. Also, look up how complex numbers are used in electrical engineering. Thus, to say that square roots of negative numbers do not exist, is false (no offense intened towards your teacher, who probably meant to say that in his/her class, complex numbers would not be taught)

√-2 =√2×√-1 But this √-1 is not a real number and so square roots with negative numbers do not exist.

They do - but only if the negative sign is outside the root. When you want to solve a square root there are always two answers - one positive and one negative. The reason for this is - x - = + so you can only have a positive value that can be rooted but that root can be either positive or negative. Remember, a square number is a number multiplied by itself so eg -2 x -2 = 4 as does 2 x 2 =4; the only way you could get a negative answer would be by multiplying a negative number by a positive number - therefore, you are not multiplying a number by itself so the result cannot be a squared number. Hope that helps.

The reason that negative square root numbers don't exist is due to the nature of you square rooting a number that is negative off itself, if you square root 2 it goes to something like 0.4412 for example while if you square -2 you would get the number -0.4412 but that can't happen as the purpose of a square root is to make it smaller while if it is negative you have made it bigger so doesn't work. sorry if that doesn't make sense

Square roots of negative real numbers do not exist in the real numbers. They do exist in the complex numbers, using the imaginary unit "I" .The terms "real" and "imaginary" are historical vestiges from a time when mathematicians were skeptical about the legitimacy and meaning of complex numbers. We say is a " square root" of y if x^2=y. Thus both+7 and -7 are square roots of 49. Therefore we have √49=+7, despite -7 also being a square root.

Negative square roots are not real numbers, but are represented by the product of the absolute value of the negative number and the imaginary unit "i". For example, the square root of -4 is 2i, while the square root of -9 is 3i.

Negative square roots are not real numbers, but are represented by the product of the absolute value of the negative number and the imaginary unit "i". For example, the square root of -4 is 2i, while the square root of -9 is 3i.

square root of negative number don't exists in real. so they are imaginary numbers. so that is why your teacher told so.

The usually not encountered in the context of real numbers. The reason for this is that the square of a real number is always a non- negative number its either positivr or zero. E.g the square of 3 is 9 . However , the rules of arithmetic change when dealing with complex numbers. In case of complex numbers the square of any number can be negative, positive or zero. E.g the square of complex number i is -1.

Hey lovely, Yes it do not exist and to deal with such number that are complex number there is imaginary number named as iota it’s an easy thing. I hope you understand.

Negative numbers doesn't have real square roots since a square is either positive or 0. If the radicand is not a perfect square i.e. the square root is not a whole number than you have to approximate the square root. The square root of negative numbers is also classified as UNDEFINED on the GED math test. In the set of real numbers, no number exists that, when multiplied by itself is a negative product. So it's UNDEFINED. But there is somthing that is called Imaginary Number denoted as "i" so the square root of -4 will be + or - 2i.

Negative square roots can't be represented in the form of a real number so that's why they are not represented. Let's take an example of 4 the square roots of √4=2. If we take -4 square roots then the result will be an imaginary number then √i = -4 = √-4 = 2 and it is an imaginary number

hi leia 1. Square of postive number is positive 2*2=4 Square of negative numbers is also positive -2*-2=4 the square of negative numbers are postive real numbers 2.The negative square roots are also exists but they are imaginary suppose we can write √(-2)=√(ⅈ^2 ) 2=ⅈ√2

Negative square roots do exist, but they are not real numbers. They are represented using imaginary numbers, which are used to extend the concept of real numbers to include the square roots of negative real numbers.

Actually there’s no sq root for negative numbers but there’s a imaginary tool to solve the problems in a bit easy way. For example; the sq root of 4 is under-root 2. But for negative number -4 u can’t take root for -2. To solve problems the imaginary tool (i) is used as -1 and solve the equations bit easier way.

This becomes imaginary number. You can make this one a positive by using i (√-1 = i), this becomes i√2.

A square root of something is an attempt to find what got multiplied with itself to get this number Eg: 12*12=144 and thus √144 =12 Now you take a negative number, -12 -12*-12= 144 again So you can never get a negative number on multiplying anything by itself (be it positive or negative) Thus you can never have √-144 I hope this answers

Your Maths teacher is meaning that only positive numbers when square rooted give real results, but a negative number does have square roots, but a negative number also means something less than zero. Think of things in terms of counting. If we count 4 sheep, we see them. Square root the 4, and we are left with 2 real sheep. But -4 means there's no physical sheep present. We can't square root something we cannot count in real ways and get real results, we have to imagine it. So we can imagine 4 sheep go in a field, square root these imaginary sheep, and we are left with 2 imagined sheep! So we use the phrase "imaginary numbers" when square rooting a negative number, a number in counting terms means we don't physically hold these. We use the letters I or j to stand for an imaginary number. Square root of -4, is now 2i (or 2j) however you like to write it. The person reading this, can now see that if we square 2, we get 4. If we square 2i, we get -4. I hope this answers your question clearly enough.

The square root of 25 is 5 multiplied by 5, but the square root of -25 cant be -5 because -5 multiplied by -5 makes 25, so the square root of -25 can't be -5.

Yes, the square root of negative numbers do not exist in real numbers domain. Although it exists in imaginary numbers. In real numbers, there is no such number which when multiplied by itself, gives us a negative numbers. e.g. there is no real number which can give us answer as -2, when multiplied by itself.

Zero has one square root which is 0. Negative numbers doesn't have real square roots since a square is either positive or 0.

negative square roots do exist, but they are not real numbers. Instead, they are part of the larger set of complex numbers that includes both real and imaginary parts.

Negative exponents do exist in mathematics, and they are an important concept in algebra and calculus. In fact, negative exponents are simply a shorthand notation for fractions with positive exponents.

Because no number times itself can equal to a negative number.

Because negative numbers doesn't have real squre roots. Squre of any positive or negative integers is only positive or zero. Squre root is not whole number. Two negative numbers multiplication is also positive.

It is true that square root of a negative number doesn't exists. Because square root of a negative number is a complex number. √-1= imaginary number( i )

Good 👍 day Leia! To answer your question. Negative square roots don't exist among the set of real numbers . This is because the square of any real number is always positive or zero, and there is no real number whose square is a negative number. However, imaginary numbers extend the notion of the real numbers to include solutions to equations that do not have real solutions. In the case of negative numbers, the imaginary unit(I) is used to represent the square root of -1, and complex numbers are used to represent the square roots of negative real numbers . Therefore, by using imaginary numbers, we can extend the concept of a square root to include negative numbers. In simpler terms, you cannot take the square root of a negative number and get a real number as the result because the square of any real number is always positive or zero. To deal with negative square roots, we use imaginary numbers. The imaginary unit (i) represents the square root of -1, and complex numbers are used to represent the square roots of negative real numbers. By extending our number system to include imaginary numbers, we can take the square root of any number, including negative ones.

Hello Lela, Negative square roots do exist, but they are considered complex numbers. A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit (i.e., the square root of -1). When we take the square root of a negative number, we get an imaginary number. For example, the square root of -9 is 3i, which is a complex number. Similarly, the square root of -4 is 2i, and the square root of -1 is i. However, when we use the term "square root" in the context of real numbers, we typically refer to the non-negative root. For example, the square root of 9 is 3, not -3. This is because the square of -3 is also 9, so both 3 and -3 are considered square roots of 9. However, when we use the term "square root" in the context of real numbers, we refer only to the non-negative root by convention.

This is because whenever a negative number is multiplied with a another negative number, the result is always positive. e.g. -2 x -2 = 4. Similarly, when two positive numbers are multiplied, the result is also positive. e.g. 2 x 2 = 4. Therefore, there is no way for a number to be multiplied with itself and result in a negative number. It will always be positive.

Square roots of negative numbers do not exist in the real number system but they do exist in complex numbers.

Negative square root do exist but it is not a real number.i.e square root of 4 is 2but square root of -4never exist in real number but it exist in complex numbe i.e square root of -4is 2i.

any number raised to the power 2 (squared) will always result in a positive number. For example: (-2)^2= 4 (2)^2= 4 That is why only positive numbers can have square roots and negative numbers cannot.

This is because every number squared(whether positive or negative), always gives a positive answer. Eg. 5^2=25 and (-5)^2=25 (when 2 negatives are multiplied together, you get a positive answer)

Square root of negative num is imaginary num, since a square is either positive or 0. If the square root is not a whole number than we have to approximate the square root.

Negative numbers doesn't have real square roots since a square is either positive or 0. If the radicand is not a perfect square i.e. the square root is not a whole number than you have to approximate the square root (unless we can keep √3 as an answer).

They exist at higher learning institutions. Imaginary numbers

They exist at higher learning institutions. Imaginary numbers

According to google: The square root of negative numbers is also classified as UNDEFINED on the GED math test. In the set of real numbers, no number exists that, when multiplied by itself is a negative product. So it's UNDEFINED. According to google: Explanation: No, we cannot find the square root of a negative number. The product of two numbers with the same sign is always positive.

No, it can’t exist because the product of two numbers with the same sign is always positive.

Explanation: No, we cannot find the square root of a negative number. The product of two numbers with the same sign is always positive.

No, we cannot find the square root of a negative number. The product of two numbers with the same sign is always positive. For the product to be negative; the signs must be opposite.

Negative square roots do exist, but they are not considered as valid solutions in the context of the real number system because the square of any real number is always non-negative.

The square root of a negative number is not a real number. This is because the square of any real number is always positive or zero. For example, the square of 2 is 4, and the square of -2 is also 4, which is a positive number. However, the square of a negative number is always positive, so there is no real number that, when squared, gives a negative number.

When we talk about negative numbers and their square roots, things get a little tricky. The thing is, when we multiply two negative numbers together, we get a positive number. So, if we were to try and find the square root of a negative number, we wouldn't be able to find two numbers that multiply to give us a negative number because two negative numbers always give us a positive one! That's why we say that negative square roots don't exist - it's not possible to find a number that, when multiplied by itself, gives us a negative number. It might seem a little confusing, but it's just the way math works!

When we talk about negative numbers and their square roots, things get a little tricky. The thing is, when we multiply two negative numbers together, we get a positive number. So, if we were to try and find the square root of a negative number, we wouldn't be able to find two numbers that multiply to give us a negative number because two negative numbers always give us a positive one! That's why we say that negative square roots don't exist - it's not possible to find a number that, when multiplied by itself, gives us a negative number. It might seem a little confusing, but it's just the way math works!

In a simple response, square roots are never used or presented because squares always result in a number that is positive or 0.

this is because a square is either positive or 0.

Negative roots do exists but they are not real numbers. The square of a positive or negative number is always positive, so there is no a real number that has a negative square. Therefore the square root of a negative number is not a real number.

I wouldn't say that negative square roots don't exist. Yet, negative square roots are not considered as real numbers (they are imaginary numbers). If you think conversely, any square of a real number is non-negative (e.g. the square of (-2) is still positive 4). For this reason, having a negative square root would not be possible to lead to a real number.

I wouldn't say that negative square roots don't exist. Yet, negative square roots are not considered as real numbers (they are imaginary numbers). If you think conversely, any square of a real number is non-negative (e.g. the square of (-2) is still positive 4). For this reason, having a negative square root would not be possible to lead to a real number.

We can not find the square root of a number because the product of a two numbers with the same sign is always positive

Negative numbers doesn't have real square roots since a square is either positive or 0. If the radicand is not a perfect square i.e. the square root is not a whole number than you have to approximate the square root (unless we can keep √3 as an answer).

They do exist, but most of the maths we learn at school are located within the Real numbers. The negative square root of a number it's an extension to the numbers called imaginary.

Negative square roots do exist, but they are considered as complex numbers. The square root of a negative number is an imaginary number and can be represented as a multiple of the imaginary unit "i", where i is defined as the square root of -1. For example, the square root of -4 can be represented as 2i, where i is the imaginary unit. This means that (2i)² = -4. However, in the context of real numbers, negative square roots are considered non-existent because the square of any real number is always non-negative. In other words, if "x" is a real number, then "x²" is always greater than or equal to 0. Therefore, there is no real number whose square is a negative number.

We can understood the meaning of square root is "reverse of square ". So square of any number will be always positive i.e. (-4) * (-4) = 16. And as we have understood that it's reverse will be it's square root so the square root of 16 will be 4 or -4. Therefore we never get a negative number by squaring any real number. That's why it's reverse also not possible i.e. the squareroot of negative number do not exist.

Because square of two number is always positive or zero. Square root with negative number is not a real number . Sqrt(-2) means we want to find an x such that x^2=-2 . It is not possible in real number system

teacher meant "real numbers" like that dont exist, but you'll learn about " imaginary" numbers later as you extend the number system these are written in the form of real numbers multiplied by the imaginary unit called “i”.

It exists, but the answer is known as a complex number which is an array of maths you probably haven’t learnt yet. If you are interested, do further maths in Alevel! Alternatively you can also understand it as because square root is the inverse of square. When you square a number, it is always positive/non-negative. Say if you square 4, which is 16. Square (-5), that would be -5 x -5 which is +25. That’s why the square root of negative numbers “doesn’t exist”. Hope that helps

Negative square roots do exist and are valid mathematical concepts. In fact, every positive real number has two square roots: one positive and one negative. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 multiplied by itself (3 x 3) equals 9. However, -3 multiplied by itself (-3 x -3) also equals 9. Therefore, both 3 and -3 are square roots of 9. In general, for any positive real number x, the two square roots are denoted as √x and -√x, where √x represents the positive square root and -√x represents the negative square root. Negative square roots are used in various mathematical applications, such as solving quadratic equations, working with complex numbers, and representing distances and measurements in physics and engineering. It's important to understand that both positive and negative square roots are valid mathematical concepts and have their own unique properties and applications.

This is because the square of any real number is always positive

Negative numbers doesn't have real square roots since a square is either positive or 0. If the radicand is not a perfect square i.e. the square root is not a whole number than you have to approximate the square root

Yes the square root of a negative numbers doesn’t exit but there is a concept called complex number. Where sqrt of -1 is called iota symbolised as ‘i’. Therefore sqrt of -2 will be 1.4142i

if you multiply a square root by itself, it creates the number - root 2 times root 2 will make 2. the root may be negative, but when you multiply two negatives it becomes positive, so you cannot - normally - have a root of a negative number, because you cannot multiply two identical numbers to get a negative; they do exist, but only as imaginary numbers. you might meet them at Higher/A level and beyond.

Leia, we get a square number when we multiply any number twice. So it means that if I have to take a square of any negative value we will get a positive value (maths rule) and if we take a square of any positive number again we will get a positive number. In conclusion, we are not able to get any value in negative while squaring so how can we take out its root? In easier words, we take out the root to find a number that is multiplied twice to get the number in the root, so it is no square roots with negative numbers will give an error.

Leia, we get a square number when we multiply any number twice. So it means that if I have to take a square of any negative value we will get a positive value (maths rule) and if we take a square of any positive number again we will get a positive number. In conclusion, we are not able to get any value in negative while squaring so how can we take out its root? In easier words, we take out the root to find a number that is multiplied twice to get the number in the root, so it is no square roots with negative numbers will give an error.

Because a square root is a number multiples by itself, so in your example that would be -2 x -2, when you multiply two negatives your answer becomes positive

Because if you square a number you won't be able to get a negative number. A square root of -2 would mean finding a number that would square to give -2 which is not possible.

If you are working with real numbers only, the square root of a negative number does exist because to get a square number, you multiply a number by itself twice. There is no negative product of two negative or positive numbers. When you study complex numbers further maths, you will be able to find the square root of a negative number eg √-2 = +/-i√2

Negative numbers doesn't have real square roots since a square is either positive or 0. If the radicand is not a perfect square i.e. the square root is not a whole number than you have to approximate the square root (unless we can keep √3 as an answer).

Negative square roots do exist if you study Further maths complex numbers, they are imaginary numbers.

In the Real Number System they don’t exist because a negative times a negative is ALWAYS a positive. Therefore, an ancient Greek mathematician named Hero invented a way to calculate the square root of a negative number by introducing the sq rt of a -1 is i. The imaginary numbers were invented and later in the Complex Number System came to be.

We define the square root of a number (x) as a number when multiplied by itslef gives gives the number (x). However, when a negative no. is multiplied by itslef it always gives a positive number therefore the sqrt of -ve numbers does not exist.

I am not being admitted to the Question and Answer function :( I spent a little time explaining to Leia how the square root of a negative number can have meaning...

They DO exist. Kind of. I am studying Further Maths at A Level and we learn about square roots of negative numbers, however they’re not real, they’re imaginary. The reason negative square roots can’t exist is because -4 x -4 = 16. So we say that the square root of 16 is + or - 4 but the square root of -16 is 4i. However its not something you learn unless you choose to study Further Maths at A Level and so at your stage of education it doesn’t really matter. Hope that helps :)

Negative numbers do not have real roots because when a negative number is multiplied by itself it yields a positive number and so is the case for a positive. therefore there exist no number such that when you multiply by itself the result is a negative. then we think of a number( imaginary number i ) such that i squared is negative.

Finding a square root of a number A relies on finding another number B such that, after multiplying B by itself, the result produced will yield A. Naturally, we often (almost always) think of the outcome of multiplying any number by itself to produce a positive number. Therefore, the idea of finding negative square roots challenges our minds and thinking in ways that are not natural - there's a natural tendency to think negative square roots do not exist in the real world. However, in a complex world, the advent of complex analysis makes it possible to discover that negative square roots do actually exist. Hope this explanation helps!

Negative times negative always makes a positive.

I am not being admitted to the Question and Answer function :( I spent a little time explaining to Leia how the square root of a negative number can have meaning...

To answer this question first we need to consider the field of numbers we are dealing with (i.e. the set of numbers under our consideration) in our case let it be R the real numbers. since the equation x^2+1=0 doesn't have a solution in the real number so the root of the negative in R can not be defined. More general if we deal with other bigger fields such as C ( the set of complex numbers) here we can define the root of the negative.

Yes. because the negative numbers cannot be represented in the form of a real number.

The negative square roots don't exist because they can't be represented in the form of a real number. Negative square roots are represented by the letter i, which represents the square root of minus one.

Minus numbers are inexistent. As much as you can multiply numbers and increase and decrease. Think about money. Think about deficiency. Hence the word negative and therefore, minus figures. Square rooting a number that does not exist cannot be possible. It is like trying to break down nothing. There are mathematical explanations of why it square root of a negative number does not exist. Happy searching :)

It is true that square roots with negative numbers don't exist because "they can't represented in the form of a real number."

It is true that square roots with negative numbers don't exist because" they can't represented in the form of a real number ". Negative square roots are represented by the letter i, which represents the square root of minus one.

Square root with negative numbers do not exit because it is represented as i (imaginary numbers ) which is not a part of real number system.

it exists for example -9, it can be represented as 3i 3i x 3i = -9

Because we do square of any number, we don't get negative number . Square is always positive hence we can get square root of positive numbers only. If you want to calculate square root of negative number, you will learn in imaginary numbers in higher classes square root(-2) will be root(2)*i, where I is imaginary number.

Negative square roots do exist, but they are not real numbers. When you take the square root of a non-negative real number, the result is a non-negative real number. For example, the square root of 4 is 2, and the square root of 9 is 3. However, when you take the square root of a negative real number, the result is not a real number. Instead, it is an imaginary number. An imaginary number is a complex number that can be written in the form a + bi, where a and b are real numbers, and i is the imaginary unit, which is defined as the square root of -1. For example, the square root of -4 can be written as 2i, because (2i)² = -4. Similarly, the square root of -9 can be written as 3i, because (3i)² = -9.

This statement is not quite right it doesn't exist in R but it does exist in an other group of nombers called C that contains R

n terms of real numbers, your maths teacher is accurate. Any real number's square in the real number system is always a positive integer. This implies that every negative number's square root is a real number. However, it is possible to define the square root of a negative number in the so-called complex number system, which also includes both actual and fictitious numbers. Any negative number can be expressed as the square root of its absolute value multiplied by "i," where "i" is an imaginary unit that can be defined as the square root of -1.

There is no real number whose square is negative. All real numbers have their squares positive so the square root of all negative real number is nonexistential

Dear! Its not like they don't exist by they are not real numbers. The square of a real number is always positive, so taking the square root of a negative number requires the introduction of imaginary numbers.

Suppose if we take -2 × -2 then we will get the answer 4 by the maths rule so it means any positive numbers square root is real but if we take the square root of -4 then it will show 2 with i means imaginary number so we don't get real number

They do exist, however not in a whole number form... As the square of a negative number will always be positive, so will the square of a positive number. Eg. Let us check √-25 We know that : 5 x 5 = 25 –5 x –5 = 25 Hence there is no solution to √-25 However, we can work it out to simplify. √-25 we can let √-1 be y √-1 = y √25 x √-1 5 x y 5y - 5y is the simplified form of √-25

Your math teacher is correct in the context of real numbers. The square root of a negative number is not defined among real numbers, since the square of any real number is non-negative. However, in the context of complex numbers, the square root of a negative number is defined. Complex numbers consist of a real part and an imaginary part, and they can be represented in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1. In the case of √-2, it can be expressed as √2i, which is a complex number with a real part of 0 and an imaginary part of √2. So, while the square root of a negative number is not defined in the context of real numbers, it is defined in the context of complex numbers.

Negative numbers doesn't have real square roots since a square is either positive or 0.We dnt have a negative square root number

Negative numbers doesn't have real square roots since a square is either positive or 0. your maths teacher is correct

Square roots don't exist as a square is either a positive or 0

The square root of a negative number does not have a real-valued answer since the square of any real integer is always positive or zero. Alternatively, we provide imaginary numbers and multiples of the square root of -1 or i.

Yes, if you have a square root number, for example square root of -4 ? Which number multiply by itself will give -4? Any number multipy by itself will give a positive number and never a negative number. Therefore there is no square root with negative number. Because any number multiply by itself will give always a positive number. Hope it does help , thank you for your interest , Anne BABAD

Because when we find the square root like root 49 the result is 7. 7*7=49. Any two negative or positive numbers will result in giving a value which is positive ,So square root with negative number does not exist

It is possible to root a negative number, however these numbers are imaginary/complex numbers which don't belong on the real axis. They are theoretical and don't follow the typical rules of real number. For example, the root of -1 = i and the root of -4 = 2i. These are imaginary numbers. Complex numbers however have a real and imaginary part to them. For example, 2+5i or 9-11i

Square roots of negative numbers do exist. However, the result will be an imaginary number. If we look at it from the reverse point of view, it is not possible to multiply 2 identical numbers and get a negative number. For example, -1 multiplied by -1 will give you 1 therefore in real terms, you cannot get the square root of -1.

Negative square roots do exist, but they are not considered as "real" numbers in the context of the real number system. In the real number system, the square of any real number is always non-negative. For example, the square of 2 is 4, and the square of -2 is also 4. However, if we try to find the square root of a negative number in the real number system, we get an imaginary number. An imaginary number is a complex number that can be expressed in the form a + bi, where "a" and "b" are real numbers, and "i" is the imaginary unit, which is defined as the square root of -1. The imaginary unit "i" has the property that i^2 = -1. For example, the square root of -9 can be written as √(-9) = √9 × √(-1) = 3i, which is an imaginary number. Similarly, the square root of -4 can be written as √(-4) = √4 × √(-1) = 2i. So, while negative square roots do exist in the context of imaginary numbers, they are not considered as "real" numbers in the real number system.

The square root of the negative number can't exist because the product of two numbers with the same size always positive.

Well you could look at this from another perspective. A square root of a negative number would exist in an imaginary plane. So, when you have square root of -2, that can be rewritten as square root(-1x2) If you take out square root (-1) that is essentially nothing but the value of i. You would probably end up getting square root (2) times i. Hope this helps

because no number times itself can equal a negative number

Think about it this way: when you multiply a negative number by itself, you get a positive number. So, you can never get a negative number by multiplying it with itself. However, it has been pointed out here that the square root of negative numbers exists in the "imaginary" plane. For all intents and purposes, imaginary numbers are simply tools which allow mathematicians and physicists to understand certain concepts and they are not in the realm of "real numbers".

Yes square roots with negative number do not exist as it can have only positive or zero. The negative in square root only exist with integrated number i.e. √-4=√i^2*2^2=2*i

Yes square roots with negative number do not exist as it can have only positive or zero. The negative in square root only exist with imaginary number i.e. √-4=√i^2*2^2=2*i

A square is either positive or zero,square root is not a whole number than you have to approximate the square root

A square is either positive or zero

It exists and considered as complex roots.

the square root of a negative number do not exist because if we take the square of a negative number, it is always positive as (-3)^2 = 9 and also 3^2 = 9, so √9 = +- 3 so we +3 and also -3 as the square root of 9, hence there is no way to get the square root of -9, thats why we use iota square as -1 and the number becomes imaginary or complex

This is because we live in a real world and so we deal with real numbers which are applicable to the real world On the other hand a negative square root will always produce imaginary numbers. Anything imaginary does not exist.

Yes square root for negative numbers doesn't exist

Negative square roots do exist in the context of complex numbers, which are numbers that include a real part and an imaginary part. However, when working with real numbers, negative square roots do not exist because the square of any real number is always non-negative (i.e., positive or zero). To see why, consider the definition of the square of a number x: x^2 = x*x. If x is positive, then the product of two positive numbers is also positive, so x^2 is positive. If x is zero, then x^2 is also zero. However, if x is negative, then the product of two negative numbers is positive, so x^2 is also positive. Therefore, when working with real numbers, the square root of a non-negative number always exists and is either positive or zero. However, the square root of a negative number is not a real number, and hence it does not exist in this context.

First off, complex numbers—i.e., numbers with both a real and an imaginary component—can have negative square roots. Second, because a square may only be positive or zero, negative integers don't actually have square roots. You must be aware that every square root has a fictional + or - that can be change as a negative or converted as a positive i.e. - * - = + Quick - * - = + + * + = + - * + = - + * - = -

The square of a negative number do exist but that notion starts a certain level of study in mathematics and you can be assured that they are very useful in our world today ( financial economics ,signal processing, AC circuit analysis ,Quantum mechanism and many others so complex numbers in a whole are important in our lives and impact them more than we think in this 21st century and surely more in other centuries to come

The square of a negative number do exist but that notion starts a certain level of study in mathematics and you can be assured that they are very useful in our world today ( financial economics ,signal processing, AC circuit analysis ,Quantum mechanism and many others so complex numbers in a whole are important in our lives and impact them more than we think in this 21st century and surely more in other centuries to come

The word square here means a number is multiplied by itself. It can also be called the root number, or index, of two. When finding the square root of a number a special symbol is used--the square root sign. The number under the sign is called the radicand. o, is there a way of taking the square root of negative numbers? Theoretically, using real numbers, it cannot be done. Two negative numbers multiplied together always produce a positive number; there are no known exceptions. The number zero is considered to be its own square root. However, mathematicians have found a way to calculate square roots of negative numbers. Any negative number can be written as a multiple of -1. For instance, -64 can be written as -1x64. So to find the square root, we write the following But wait, what is the square root of -1? There is no real square root of -1, but we assume that in some universe there is such an integer, and it is given the name i, or iota, and it is defined as . Because it does not exist in real numbers, it is called an imaginary number. It may seem odd to have to create imaginary numbers, but they are necessary in electrical problems, radar, brain wave studies, and other higher mathematical studies.

Actually, the square root of a negative number exists, but it is not a real number. For example the square root of -1 is the (imaginary) number i which belongs to a the set of complex numbers that is properly bigger than the set of real numbers and you probably will deal with these kind of numbers in college or university. In secondary school and high school, we just deal with the real numbers and we know that the square of every real number x is always a positive number (or zero in case x=0) and it is never a negative number. So, there is no real number whose square is negative. This means that the square root of a negative number does not exists (in the set of real numbers).

Leaving out the imaginary number(i), square of any two real numbers must be positive. Both the Square of (x) and Square of (-x) are the same. Likewise, square of any real number is positive. Hence, the square roots of negative numbers does not exist.

Square root of a negative is an imaginary number that is iota. So, square root of a negative number exists not in real numbers but in complex numbers

Square root of a negative number does not exist because square is either positive or zero. Yes, square root of a negative exist not in real numbers but in complex number. Square root of a negative is iota which can't be plotted on real number line but we can plot it in imaginary axis that is vertical axis of acomplex plane

Because no number times itself can equal a negative number.

Yes, it does not exist because square root of negative numbers is imaginary number, so it is undefined. Square root is either 0 or positive number.

If u look at every square number you will find that their square root is always a positive number, square root of 4 is 2, square root of 9 is 3, etc. This is because every square number is formed by a number multiplied by itself. if you were to take any negative number and then square it i.e multiply it by itself, you would find it to always result in a positive number because two negatives when multiplied or divided always result in a positive. So in actual fact every positive square has two square roots, the square root and its negative counterpart but we most often ignore the negative. The square root of any negative number will always involve what's called imaginary numbers which is a whole section of maths involving numbers that effectively don't exist but are very useful with complex forms of logic.

Square numbers can only be positive numbers because every square number is formed by a positive or negative number multiplied by itself. 2 times 2 is 4 and -2 times -2 is also 4. This is the case for every square number. So square rooting only works on positive numbers if you want a real result. When you square root a negative number the result always includes an imaginary number which is a number that effectively doesn't exist but is very useful when working with complex logic.

In general, when someone is asking for a square root, they are seeking the positive value. This is called the principal square root. However, square roots can also be negative. Thus, the number -6 can be a square root of the number 36, just not a principal square root. So the negative square root is the same number as the principal square root, but the negative version. The negative square "squared" will give the same positive result as the principal square root, for instance, 3 • 3 = 9 and -3• --3 = 9

Square roots of negative numbers are not numbers. The student can verify this. Choose any number on the number line. Square it. The answer is positive.

Negative square root does not exist

In the context of real numbers, your maths teacher is accurate. The square root of a negative number does not exist in the set of real numbers. However, the square root of a negative number exists in the set of complex numbers, which includes real and imaginary numbers. Complex numbers, in reality, are defined as a combination of a real number and an imaginary number, with the imaginary unit denoted by the letter "i." For instance, "i" is the square root of -1. While your teacher is correct in the context of real numbers, the concept of negative square roots is correct in the context of complex numbers.

We cannot find the square root of a negative number. The product of two numbers with the same sign is always positive.

In the world of "Real numbers" We can't find a number x , such that x*x = -2. If x is positive, x*x is positive If x is negative, x*x is positive So it can't be negative. There's a branch of mathematics called Complex Analysis, which allows the existence of negative square roots, but it gets a bit more.... Complex :)

Negative roots may exist but they are not real because squares is either positive or 0. It will be a problem to solve negative roots but there is a possibility to solve them to some extent. that's why we say negative square roots do not exit.

Negative square roots do exist in the realm of complex numbers, but they do not exist in the real number system. In the real number system, a square root is defined as the non-negative number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 times 3 equals 9. By definition, the square root of a positive number is always positive. However, when we extend the real number system to include complex numbers, we introduce the concept of the imaginary unit, denoted by the letter "i", which is defined as the square root of -1. In the complex number system, a square root of a negative number is defined as a complex number whose square is equal to the original negative number. For example, the square root of -4 is 2i, because (2i) times (2i) equals -4. In summary, negative square roots do not exist in the real number system, but they do exist in the complex number system. The reason for this is that the real number system is only a subset of the larger complex number system, and the rules for square roots are different in the two systems.

Negative numbers doesn't have real square roots since a square is either positive or 0. If the radicand is not a perfect square i.e. the square root is not a whole number than you have to approximate the square root (unless we can keep √3 as an answer).

Negative square roots do exist, but they are considered to be complex numbers, which are not part of the real number system that we use in everyday mathematics. When we take the square root of a positive number, we get two solutions, one positive and one negative, such as √4 = ±2. However, when we try to take the square root of a negative number, such as √-4, there is no real number that can satisfy this equation, since the square of any real number is always non-negative. Instead, we use the imaginary unit i, defined as the square root of -1, to represent the square root of a negative number. So, √-4 can be expressed as 2i

As we know that two negative numbers on multiplying gives a positive number. So, squaring a number means multiplying a number with the number itself. That is 2² = 2 x 2 = 4. Similarly, (-3)² = (-3) x (-3) = 9. Hence squaring a number cannot be negative which indicates that square root of a negative number cannot exist.

you can't get the square root of a negative number because, when you take the square root of a number that is negative, you can't change it back to the negative number except they have different signs when you take the square of it, i.e taking the square root of negative 64 (√-64) will give you (-8*+8) and not (-8*-8) or (+8*+8) but when taking the square root of a positive number it's different, i.e (√36)= +6*+6 though you can find the square root of questions like -√64 or -√36

Negative square root does not have real square ròot since a square is either positive or 0.

Yes. Negative numbers indeed do not have square roots because these would give you imaginary numbers.

Square root of negative number results in imaginary numbers that we called complex number. We can say that negative square root is actually iota (i) which is an imaginary number. you can write square root of -2 as square root 2 iota

while the square root of a negative number does not exist within the realm of real numbers, it can be defined using imaginary numbers in the field of complex numbers.

Negative square roots do not exist in real number - form but they exist in the form of Imaginary number . When we take the square root of a positive number, we get two possible answers, one positive and one negative. For example, the square root of 25 is 5, but we can represent it as -5 also because (-5)² is also equal to 25. However, when we take the square root of a negative number, we run into a delema. The square of any real number is always positive, so there is no real number whose square is negative. For example, the square root of -25 cannot be a real number, because there is no real number which can have two identical factory of -25 if I think (-5)*(-5) =25 that is not equal to -25

The numbers are broadly two types: real numbers and imaginary (x+iy) numbers. In this, x and iy are two real and imaginary parts; x and y are real numbers, and i is imaginary. Interestingly, all real numbers are imaginary numbers and not vice versa. Both numbers are bridged by the relation i^2 = -1 i.e. sq.rt (-1) = i. Imaginary numbers have special applications in Electrical and Electronics Engineering, and mainly in Quantum mechanics/Physics.

Hi, square roots with negative numbers do exist that's a bit more on the advanced side of things. When you get to square roots of negative numbers those are complex numbers. So the reason why your teacher might have told you that is it might have not been relevant to the level of math your were doing at the time.

Hi, square roots with negative numbers do exist that's a bit more on the advanced side of things. When you get to square roots of negative numbers those are complex numbers. So the reason why your teacher might have told you that is it might have not been relevant to the level of math your were doing at the time.

A negative square does exist but they are not real numbers called complex numbers for example √-2= √2×√-1 (√-1=i)=√2i

Negative square roots do exist, but they are not real numbers. This is because when we square a negative number, the result is a positive number. For example, (-2)^2 equals 4. Therefore, there is no real number that when squared will give a negative result. This is why the square root of a negative number is defined using imaginary numbers, which involve the square root of -1, represented by the symbol 'i'.

Real numbers do not have negative square roots. Negative numbers cannot be square roots since they cannot be multiplied by themselves. However, complex numbers using unit do have negative square roots. The letter i, which stands for the square root of -1, is used to denote negative square roots.

Hi Leia! The simple answer is that any number being multiplied with itself will always be a positive. However we can use values such as i (imaginary numbers) to create a value for the square roots of negative numbers.

Square numbers can be positive or negative, however negative square roots don’t exist as -2^2, or -2 x -2 = 4, as two negatives make a positive, so a negative square gives a positive answer. However a square root can give a positive or negative solution as √25 can be 5^2 or -5^2 which both give the answer of 25.

Hi Leia, that's an interesting question. To help you understand it, I want you to think of the number under the radical as the result of another number being squared. For example, 3 squared is 9, and the square root of 9 is 3. So, if the number under the radical is always obtained by squaring another number, it cannot be negative. No number will multiply itself to turn into a negative number. Example: -2 x -2 = 4 and 2 x 2 = 4. In all cases, the result will be positive. But what about -2? We cannot look for the square root of -2 because no number can multiply itself to give -2. I hope that was helpful.