Question

Question 12
The number obtained on rationalising the denominator of $\frac{1}{\sqrt{7}-2}$ is

A) $\frac{\sqrt{7}+2}{3}$
B) $\frac{\sqrt{7}-2}{3}$
C) $\frac{\sqrt{7}+2}{5}$
D) $\frac{\sqrt{7}+2}{45}$

Answer 1

The answer is A.
$\frac{1}{\sqrt{7}-2}=\frac{1}{\sqrt{7}-2}.\frac{\sqrt{7}+2}{\sqrt{7}+2}\_[Multiplyingnumberatoranddenominatorby\sqrt{7}+2]$
$=\frac{\sqrt{7}+2}{(\sqrt{7}{)}^2-(2{)}^2}=\frac{\sqrt{7}+2}{7-4}=\frac{\sqrt{7}+2}{3}$ [Using identity (a -b) (a + b) =$a^2-b^2]$