Compound Surds

Algebra Level 2

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 \(b-a\).