What is the square root of $(-5)^2$?

Question

Is this statement true?

$$\sqrt{(-5)^2} = -5$$

Answer 1

No it is not.

You have

$$\sqrt{(-5)^2}=\sqrt{(-5)\times (-5)}=\sqrt{25}=5.$$

Not $-5$.

Answer 2

No: The radical sign usually denotes the non-negative branch of the square root, so $$ \sqrt{x^{2}} = |x|\quad\text{ for all real $x$.} $$ Consequently, $\sqrt{(-5)^{2}} = 5$.

Answer 3

$$\sqrt{(-x)^2} = |x|$$

$$(\sqrt{x})^2 = x$$