Rationalise the denominators of each of the following:$ \frac{\sqrt{2}}{\sqrt{5}} $

Given:

\( \frac{\sqrt{2}}{\sqrt{5}} \)

To do: 

We have to rationalise the denominator of the given expression.

Solution:

We know that,

Rationalising factor of a fraction with denominator ${\sqrt{a}}$ is ${\sqrt{a}}$.

Rationalising factor of a fraction with denominator ${\sqrt{a}-\sqrt{b}}$ is ${\sqrt{a}+\sqrt{b}}$.

Rationalising factor of a fraction with denominator ${\sqrt{a}+\sqrt{b}}$ is ${\sqrt{a}-\sqrt{b}}$.

Therefore,

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

$=\frac{\sqrt{2\times5}}{(\sqrt{5})^2}$

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

Hence, $\frac{\sqrt{2}}{\sqrt{5}}=\frac{\sqrt{10}}{5}$.