Question

Rationalise the denominator of $\frac{1}{\sqrt{7}-\sqrt{6}}$.

• A. $\sqrt{7}+\sqrt{6}$
• B. $\sqrt{7}-\sqrt{6}$
• C. $\sqrt{6}-\sqrt{7}$
• D. None of these

Answer 1

The correct option is A $\sqrt{7}+\sqrt{6}$

As given ,$\frac{1}{\sqrt{7}-\sqrt{6}}$
[Multiply and divide by $\sqrt{7}+\sqrt{6}$]
$=\frac{1}{\sqrt{7}-\sqrt{6}}\times \frac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}}$
$=\frac{\sqrt{7}+\sqrt{6}}{{\left(\sqrt{7}\right)}^2-{\left(\sqrt{6}\right)}^2}$
$=\frac{\sqrt{7}+\sqrt{6}}{7-6}$
$=\sqrt{7}+\sqrt{6}$