Question

Under root 11 - under root 7 divided by under root 11 + under root 7. Rationalise it

Answer 1

Dear student,

$$\begin{gathered} Toevaluate: \\ \frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}=\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}\times \frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}-\sqrt{7}} \\ =\frac{{\left(\sqrt{11}-\sqrt{7}\right)}^2}{{\left(\sqrt{11}\right)}^2-{\left(\sqrt{7}\right)}^2}......\left[\left(a^2-b^2\right)=\left(a+b\right)\left(a-b\right)\right] \\ =\frac{11+7-2\sqrt{77}}{11-7} \\ =\frac{18-2\sqrt{77}}{4}=\frac{2\left(9-\sqrt{77}\right)}{4}=\frac{9-\sqrt{77}}{2} \end{gathered}$$

Regards