Question

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

Answer 1

Solution:-

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

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

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

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

$\Rightarrow =\frac{\sqrt{10}}{5}$