Square Root of Sum as Sum of Square Roots

Theorem
Let $a, b \in \R, a \ge b$.

Then:
 * $\sqrt {a + b} = \sqrt {\dfrac a 2 + \dfrac {\sqrt {a^2 - b^2}} 2} + \sqrt {\dfrac a 2 - \dfrac {\sqrt {a^2 - b^2}} 2}$