Is $\sqrt{x^2}$ even or odd? Is the function $x\mapsto \sqrt{x^2}$ even or odd?
Mentioning the square root does not have negative sign, 
$\sqrt{x^2} = \pm x$
As it is clear LHS is even and RHS is odd for both sign, which one is true?

It’s the same thing as the absolute value of X, which is even. Why? Because squaring and then square rooting any real quantity keeps it the same but makes positive (from when we squared it).
