Answer
See below.
Work Step by Step
I use the hint in my solution:
$b-a=(\sqrt b+\sqrt a)(\sqrt b-\sqrt a)$. $(\sqrt b-\sqrt a)\gt0$ and $\sqrt a\gt0,\sqrt b\gt0$, thus $(\sqrt b+\sqrt a)\gt0$, thus their product is also positive. Thus, the result has been proved.