OME 1990 Problem 1

Prove that $\sqrt{x}+\sqrt{y}+\sqrt{xy}$ is equal to $\sqrt{x}+\sqrt{y+xy+2y\sqrt{x}}$

and compare the numbers $\sqrt{3}+\sqrt{10+2\sqrt{3}}$ and $\sqrt{5+\sqrt{22}}+\sqrt{8- \sqrt{22}+2\sqrt{15-3\sqrt{22}}}$ .