Question

Rationalise the denominator and simplify:

If $\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ is $4+\sqrt{m}$, then $m$ is ?

Answer 1

We rationalize the denominator, $\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\ast \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\frac{5+3+2\sqrt{15}}{5-3}=\frac{8+2\sqrt{15}}{2}=4+\sqrt{15}$

$\therefore$ value of $m=15$