Question

Rationalise root 11+ root 5 divided by root 11- root 5.

Answer 1

$$\begin{gathered} \frac{\sqrt{11}+\sqrt{5}}{\sqrt{11}-\sqrt{5}} \\ =\frac{\sqrt{11}+\sqrt{5}}{\sqrt{11}-\sqrt{5}}\times \frac{\sqrt{11}+\sqrt{5}}{\sqrt{11}+\sqrt{5}} \\ =\frac{{\left(\sqrt{11}+\sqrt{5}\right)}^2}{{\left(\sqrt{11}\right)}^2-{\left(\sqrt{5}\right)}^2} \\ =\frac{{\left(\sqrt{11}\right)}^2+{\left(\sqrt{5}\right)}^2+2\times \sqrt{11}\times \sqrt{5}}{11-5} \\ =\frac{11+5+2\sqrt{55}}{6} \\ =\frac{16+2\sqrt{55}}{6} \\ =\frac{2\left(8+\sqrt{55}\right)}{6} \\ =\frac{8+\sqrt{55}}{3} \end{gathered}$$