How to compare numbers $\sqrt{5}-\sqrt{3}$ and $\sqrt{8-2\sqrt{15}}$

Question

How to compare the following numbers without using the calculator? $\sqrt{5}-\sqrt{3}$ and $\sqrt{8-2\sqrt{15}}$

Answer 1

Hint:

$$\sqrt5-\sqrt3\ge\sqrt{8-2\sqrt{15}}\iff8-2\sqrt{15}\ge8-2\sqrt{15}\ldots$$

Answer 2

As $(\sqrt 5-\sqrt 3)^2=5+3-2\sqrt {15}$ they are equal