Compound Surds

Algebra Level 1

Using the fact that $(\sqrt{x}+\sqrt{y})^2=x+y+2\sqrt{xy}$ , find the square root of $5+\sqrt{24}$ .
This number can be expressed in the form $\sqrt{a}+\sqrt{b}$ , where $a\leq{b}$ .

Find the value of $b-a$ .