Existence of Square Roots of Positive Real Number

Theorem
Let $x \in \R_{\ge 0}$ be a positive real number.

Then:
 * $\exists y_1 \in \R_{\ge 0}: {y_1}^2 = x$
 * $\exists y_2 \in \R_{\le 0}: {y_2}^2 = x$