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

Given:

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

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,

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

$=\frac{(\sqrt{2\times3}+\sqrt{5\times3})}{(\sqrt{3})^2}$

$=\frac{\sqrt{6}+\sqrt{15}}{3}$

Hence, $\frac{\sqrt{2}+\sqrt{5}}{\sqrt{3}}=\frac{\sqrt{6}+\sqrt{15}}{3}$.