Question

Rationalise the denominator of $\frac{1}{\sqrt{5}-2}$

Answer 1

Given expression

$\frac{1}{\sqrt{5}-2}$

To rationalize it we have to multiply the denominator and numerator by $\frac{\sqrt{5}+2}{\sqrt{5}+2}$

We have to use identity here $(a+b)(a-b)=a^2-b^2$

$$\begin{gathered} \Rightarrow \frac{1}{(\sqrt{5}-2)}\times \frac{\sqrt{5}+2}{(\sqrt{5}+2)}=\frac{\sqrt{5}+2}{{\left(\sqrt{5}\right)}^2-2^2} \\ =\frac{\sqrt{5}+2}{5-4}=\sqrt{5}+2 \end{gathered}$$

Hence we get $\sqrt{5}+2$ after rationalization.