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

On rationalising the denominators of both the terms, we get:
$\frac{1}{\sqrt{6}}+\frac{1}{\sqrt{5}}$ = $\frac{\sqrt{6}}{6}+\frac{\sqrt{5}}{5}$

On simplifying this by taking the L.C.M of both the denominators,
$\frac{\sqrt{6}}{6}+\frac{\sqrt{5}}{5}$= $\frac{5\sqrt{6}+6\sqrt{5}}{30}$