Explain why the square root of a negative number is not a real number?

Answer 1

because no number can be squared to get a positive number except i (imaginary number). i^2 equals -1.

Answer 2

Well, a square root just means that the answer squared is the number in the square root. For example, the square root of 4 is 2, because 2 squared equals 4.

Now, try to think of a real number that, when squared, equals a negative number. Impossible, huh? That's why the square root of a negative number is not a real number.

Answer 3

This is a great question, and it is asked by algebra students more often than you might think.
When we are looking for a square root of a number, we are asking to find a number that when multiplied by itself gives the original number.
For example, when we are looking for the square root of 25, we are asking " what number multiplied by itself, gives the answer 25?"
There are two answers that will do this: 5 and -5.
That means that 5*5 = 25. And (-5)(-5) = 25. And we may not use one of each.

If we are looking for the square root of -25, we are asking ourselves the same question as we asked before: What number multipied by itself will give us -25. If we choose 5, we have this result: 5*5 = 25. If we choose (-5)(-5), we still get 25, and it is positive because as you know the product of two negative numbers is always positive.
Now you are probably thinking, "let's just use one of each,
5 and -5. That will give us -25. It sure will, but our requirement for a square root demands that both numbers be the same. And
5 and -5 are two DIFFERENT numbers, no matter how much you think they look alike.
So the square root of a negative number is not real. (We call them imaginary.)

Answer 4

I'm sure mathematicians the world over will be relieved to hear that...

Whatever teacher/instructor posed that question, on their next test or quiz that has anything to do with the square root of a negative number write in that you can't answer that as it isn't a "real" number.

(And yes, I know a negative x a negative = a positive, but it's still a number.)

Answer 5

If you think about it, you can take any number and square it and the answer will never be negative. Any negative number squared comes out positive because you are multiplying two negative numbers.

To get the square root of a negative number, you need to use i which is imaginary.
i^2 = -1
So if you wanted the square root of -16, you would get 4i.
4i^2 = 4i * 4i = 16(i^2) = 16(-1) = -16

Answer 6

x = sqrt(-4)
x^2 = -4

anything squared is always positive, so the square root of a negative number is not real

Answer 7

It is because you can't multiply two identical negative numbers together and get a negative result... real numbers can't do that. Therefore, the result is "imaginary" like you have to pretend what the number would be....

Answer 8

because a negative times a negative always equals a positive. Theres no number that can be multiplied by itself to become a negative number.

Answer 9

there is no such thing as a square root of a negative number

Answer 10

because you cant square a number, be it positive or negative, and get a negative result.