Rationalise the denominators of each of the following:$ \frac{3}{2 \sqrt{5}} $

Given:

\( \frac{3}{2\sqrt{5}} \)

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,

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

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

$=\frac{3\sqrt{5}}{2\times5}$

$=\frac{3\sqrt{5}}{10}$

Hence, $\frac{3}{2\sqrt{5}}=\frac{3\sqrt{5}}{10}$.