Question

Rationalize the denominator of the following-
$\frac{\sqrt{10}+\sqrt{15}}{\sqrt{2}}$

Answer 1

Solution:-

$\frac{\sqrt{10}+\sqrt{15}}{\sqrt{2}}$

As we know that the rationalization factor for $\frac{1}{\sqrt{a}}$ is $\sqrt{a}$.

$\therefore \frac{\sqrt{10}+\sqrt{15}}{\sqrt{2}}=\frac{\sqrt{10}+\sqrt{15}}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

$\Rightarrow =\frac{(\sqrt{10}+\sqrt{15})\sqrt{2}}{{\left(\sqrt{2}\right)}^2}$

$\Rightarrow =\frac{(\sqrt{10}\times \sqrt{2}+\sqrt{15}\times \sqrt{2})}{2}$

$\Rightarrow =\frac{\sqrt{20}+\sqrt{30}}{3}$

$\Rightarrow =\frac{\sqrt{2\times 2\times 5}+\sqrt{30}}{3}$

$\Rightarrow =\frac{2\sqrt{5}+\sqrt{30}}{3}$