Domain of Real Square Root Function

Theorem
The domain of the real square root function is the set of positive real numbers $\R_{\ge 0}$:
 * $\left\{ {x \in \R: x \ge 0}\right\}$

Proof
From Square of Real Number is Non-Negative:
 * $\forall x \in \R: x^2 \ge 0$

Hence the result by definition of domain.