Question

Do negative numbers have positive square roots?

Answer 1

Answer: yes

Step-by-step explanation:

Answer 2

Answer: not exactly

Step-by-step explanation:

If you put a negative number in a square root you would end up with an error on the calculator. Thats because you end up with an imaginary number since a negative inside a square root can never be calculated, its simply not possible because in order for a negative number to form, a positive number must always be multiplied to a negative number. So people came up with the concept of i:

$\sqrt{-1}$ = i

So something like $\sqrt{-4}$ can be simplified like:

$\sqrt{4}$ * $\sqrt{-1}$

 2 * i

  2i

But if you're talking about squares like exponent wise, then yes

something like $(-2)^{2}$ will always be positive, but you have to be careful with the parentheses.

There is a difference btw $(-2)^{2}$ and$-2^{2}$

$(-2)^{2}$ = 4 because you are multiplying (-2)(-2)

but

$-2^{2}$ = -4 because you are multiplying -(2)(2)