Question

Which of the following is equivalent to $\frac{1}{\sqrt{6}}+\frac{1}{\sqrt{5}}$ ?

• A. $\frac{5\sqrt{6}-6\sqrt{5}}{30}$
• B. $\frac{\sqrt{6}\sqrt{5}}{30}$
• C. $\frac{5\sqrt{6}+6\sqrt{5}}{30}$
• D. $\frac{11}{30}$

Answer 1

The correct option is C

$\frac{5\sqrt{6}+6\sqrt{5}}{30}$

Rationalizing the given expression :
$\frac{1}{\sqrt{6}}+\frac{1}{\sqrt{5}}$

On taking the L.C.M of both the denominators,
$\Rightarrow$ $\frac{(\sqrt{5}+\sqrt{6})\left(\sqrt{30}\right)}{\left(\sqrt{30}\right)\left(\sqrt{30}\right)}$

On solving, we get
$\frac{\left(\sqrt{5}\right)\left(\sqrt{30}\right)+\left(\sqrt{6}\right)\left(\sqrt{30}\right)}{\left(\sqrt{30}\right)\left(\sqrt{30}\right)}$
=$\frac{5\sqrt{6}+6\sqrt{5}}{30}$