Question

Rationalise the denominator and simplify $\frac{3}{\sqrt{5}-\sqrt{3}}$

Answer 1

$\frac{3}{\sqrt{5}-\sqrt{3}}$ where $\sqrt{5}-\sqrt{3}$ is the denominator.

Now, R.F of $\sqrt{5}-\sqrt{3}$ is $\sqrt{5}+\sqrt{3}$
$\therefore \frac{3}{\sqrt{5}-\sqrt{3}}=\frac{3}{\sqrt{5}-\sqrt{3}}\times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}$
$=\frac{3(\sqrt{5}+\sqrt{3})}{(\sqrt{5}{)}^2-(\sqrt{3}{)}^2}=\frac{3(\sqrt{5}+\sqrt{3})}{5-3}=\frac{3(\sqrt{5}+\sqrt{3})}{2}$
$\therefore \frac{3}{\sqrt{5}-\sqrt{3}}=\frac{3(\sqrt{5}+\sqrt{3})}{2}$