Question

Rationalize the denominator of $\frac{5}{\sqrt{3}+\sqrt{5}}.$

Answer 1

$\frac{5}{\sqrt{3}+\sqrt{5}}$

$\Rightarrow \frac{5}{\sqrt{3}+\sqrt{5}}\times \frac{\sqrt{3}-\sqrt{5}}{\sqrt{3}-\sqrt{5}}$

$\Rightarrow \frac{5\times (\sqrt{3}-\sqrt{5})}{(\sqrt{3}{)}^2-(\sqrt{5}{)}^2}$

$\Rightarrow 5\times \frac{\sqrt{3}-\sqrt{5}}{(3-5)}$

$\Rightarrow 5\times \frac{\sqrt{3}-\sqrt{5}}{(-2)}$

$\Rightarrow -\frac{5}{2}(\sqrt{3}-\sqrt{5})$