Question

Rationalise the denominator of each of the following:
$\frac{1}{\left(\sqrt{6}-\sqrt{5}\right)}$

Answer 1

On multiplying the numerator and denominator of the given number by $\sqrt{6}+\sqrt{5}$, we get:
$$\begin{gathered} \frac{1}{\sqrt{6}-\sqrt{5}}=\frac{1}{\sqrt{6}-\sqrt{5}}\times \frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}} \\ =\frac{\sqrt{6}+\sqrt{5}}{{\left(\sqrt{6}\right)}^2-{\left(\sqrt{5}\right)}^2} \\ =\frac{\sqrt{6}+\sqrt{5}}{6-5} \\ =\sqrt{6}+\sqrt{5} \end{gathered}$$