Rationalise the denominators of each of the following:
$ \frac{3}{\sqrt{5}} $

Given:

\( \frac{3}{\sqrt{5}} \)

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,

$\frac{3}{\sqrt{5}}=\frac{3}{\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}$

$=\frac{3\sqrt{5}}{(\sqrt{5})^2}$

$=\frac{3\sqrt{5}}{5}$.

Hence, $\frac{3}{\sqrt{5}}=\frac{3\sqrt{5}}{5}$.