Question

4 /root 7 + root 3 .rationalise the denominator of

Answer 1

Dear Student,

$$\begin{gathered} \frac{4}{\sqrt{7}+\sqrt{3}}\times \frac{\sqrt{7}{\displaystyle -}\sqrt{3}}{\sqrt{7}{\displaystyle -}\sqrt{3}} \\ \left[\mathbf{U}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{}{\mathbf{a}}^{\mathbf{2}}\mathbf{-}{\mathbf{b}}^{\mathbf{2}}\mathbf{=}\left(\mathbf{a}\mathbf{-}\mathbf{b}\right)\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)\right] \\ =\frac{4\left(\sqrt{7}-\sqrt{3}\right)}{{\displaystyle {\left(\sqrt{7}\right)}^2}{\displaystyle -}{\displaystyle {{\displaystyle \left(\sqrt{3}\right)}}^2}} \\ =\frac{4\left(\sqrt{7}-\sqrt{3}\right)}{7-3} \\ =\sqrt{7}-\sqrt{3} \end{gathered}$$

Regards