Question

Rationalise the denominator of each of the following:
$\frac{1}{\left(\sqrt{5}-2\right)}$

Answer 1

On multiplying the numerator and denominator of the given number by $\sqrt{5}+2$, we get:
$$\begin{gathered} \frac{1}{\sqrt{5}-2}=\frac{1}{\sqrt{5}-2}\times \frac{\sqrt{5}+2}{\sqrt{5}+2} \\ =\frac{\sqrt{5}+2}{{\left(\sqrt{5}\right)}^2-{\left(2\right)}^2} \\ =\frac{\sqrt{5}+2}{5-4} \\ =\frac{\sqrt{5}+2}{1} \\ =\sqrt{5}+2 \end{gathered}$$