Question

Simplify $\frac{1}{\sqrt{3}+\sqrt{5}}$ by rationalizing the denominator.

Answer 1

Here the denominator is $\sqrt{3}+\sqrt{5}$. So, the rationalizing factor is $\sqrt{3}-\sqrt{5}$
$\frac{1}{\sqrt{3}+\sqrt{5}}=\frac{1}{\sqrt{3}+\sqrt{5}}\times \frac{\sqrt{3}-\sqrt{5}}{\sqrt{3}-\sqrt{5}}$
$=\frac{\sqrt{3}-\sqrt{5}}{(\sqrt{3}{)}^2-(\sqrt{5}{)}^2}=\frac{\sqrt{3}-\sqrt{5}}{3-5}$
$=\frac{\sqrt{3}-\sqrt{5}}{-2}=\frac{\sqrt{5}-\sqrt{3}}{2}$