Question

Rationalise the denominators of the following:
$\frac{1}{\sqrt{7}-2}$

Answer 1

Multiplying numerator and denominator by$\sqrt{7}+2\frac{1}{\sqrt{7}-2}\frac{\sqrt{7}+2}{\sqrt{7}+2}=\frac{\sqrt{7}+2}{(\sqrt{7}{)}^2-(2{)}^2}[\therefore (a-b\left)\right(a+b)=a^2-b^2]\frac{\sqrt{7}+2}{7-4}=\frac{\sqrt{7}+2}{3}$
Now, denominator is rationalised.