Question

Simplify $\frac{1}{8-2\sqrt{5}}$ by rationalizing the denominator.

Answer 1

Here the denominator is $8-2\sqrt{5}$. The rationalizing factor is $8+2\sqrt{5}$
$\frac{1}{8-2\sqrt{5}}=\frac{1}{8-2\sqrt{5}}\times \frac{8+2\sqrt{5}}{8+2\sqrt{5}}$
$=\frac{8+2\sqrt{5}}{8^2-(2\sqrt{5}{)}^2}=\frac{8+2\sqrt{5}}{64-20}$
$=\frac{8+2\sqrt{5}}{44}=\frac{2(4+\sqrt{5})}{44}=\frac{4+\sqrt{5}}{22}$