Why is square root of x squared = absolute x?

Question

Is it because absolute x = -x and x?

Answer 1

Wellt the so calles abs: R -> R^+_0 function assigns every x its absolute value hence a positive number or zero.

Squaring a number always yields s.th. positive as a result. It follows the statement.

Answer 2

Yes, since (-x)^2 or x^2 both yield x^2, the square root of X^2 = IxI = absolute value of x.