Rationalise the denominators of each of the following:$ \frac{1}{\sqrt{12}} $

Given:

\( \frac{1}{\sqrt{12}} \)

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,

$\frac{1}{\sqrt{12}}=\frac{1}{\sqrt{3\times4}}$

$=\frac{1}{\sqrt{3\times2^2}}$

$=\frac{1}{2\sqrt{3}}$

$=\frac{1}{2\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}$

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

$=\frac{\sqrt{3}}{2\times3}$

$=\frac{\sqrt{3}}{6}$

Hence, $\frac{1}{\sqrt{12}}=\frac{\sqrt{3}}{6}$.