Square Root of Sum as Sum of Square Roots/Proof 2

Proof
From Sum of Square Roots as Square Root of Sum:
 * $\sqrt p + \sqrt q = \sqrt {p + q + \sqrt {4pq}}$

Let
 * $p = \dfrac a 2 + \dfrac {\sqrt {a^2 - b^2}} 2$,
 * $q = \dfrac a 2 - \dfrac {\sqrt {a^2 - b^2}} 2$.

Then

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