Simplification of Surds

Let numerator $N = \sqrt{\sqrt{5}+2} + \sqrt{\sqrt{5}-2}$. $N^2 = (\sqrt{5}+2) + (\sqrt{5}-2) + 2\sqrt{(\sqrt{5})^2 - 4} = 2\sqrt{5} + 2 = 2(\sqrt{5}+1)$. $N = \sqrt{2}\sqrt{\sqrt{5}+1}$. Thus, $\frac{N}{\sqrt{\sqrt{5}+1}} = \sqrt{2}$.