***please explain****?

Question

Is (sq rt of x)^2=x an identity (true for all nonnegative values of x)?

Answer 1

It's true for all NON-NEGATIVE values of x, but it's not true for all x.

In fact, it's another way to define the absolute value function:

| x | = √(x²) = x if x ≥ 0, -x if x < 0

Example:

| -1 | = √((-1)²) = 1

Answer 2

| x | = √(x²) = x if x ≥ 0, -x if x < 0

Answer 3

not at all
the sqrt(x) is NOT defined for x negative. .
so your "identity" is actually an expression that does NOT make sense for x<0 .