Question

Rationalize the denominator of the following-
$\frac{\sqrt{2}+\sqrt{5}}{\sqrt{3}}$

Answer 1

$\frac{\sqrt{2}+\sqrt{5}}{\sqrt{3}}$

As we know that the rationalization factor for $\frac{1}{\sqrt{a}}$ is $\sqrt{a}$.

$\therefore \frac{\sqrt{2}+\sqrt{5}}{\sqrt{3}}=\frac{\sqrt{2}+\sqrt{5}}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}$

$\Rightarrow =\frac{(\sqrt{2}+\sqrt{5})\sqrt{3}}{{\left(\sqrt{3}\right)}^2}$

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

$\Rightarrow =\frac{\sqrt{6}+\sqrt{15}}{3}$