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

$\frac{1}{\sqrt{7}-2}$

$\text{[Multiplying numerator and denominator by}\sqrt{7}+2]$

$=\frac{1}{\sqrt{7}-2}\left(\frac{\sqrt{7}+2}{\sqrt{7}+2}\right)$

$=\frac{\sqrt{7}+2}{(\sqrt{7}{)}^2-(2{)}^2}=\frac{\sqrt{7}+2}{7-4}=\frac{\sqrt{7}+2}{3}\left[Usingtheidentity\right(a-b\left)\right(a+b)=a^2-b^2]$