Question

Rationalise the denominator square root 5 + square root 3 / square root 5- square
root 3

Answer 1

Answer:

$\frac{8 + 2\sqrt{5} \sqrt{3}}{2}$

Step-by-step explanation:

$\frac{\sqrt{5} + \sqrt{3}}{ \sqrt{5} - \sqrt{3}} \\= \frac{\sqrt{5} + \sqrt{3}}{ \sqrt{5} - \sqrt{3}} X \frac{\sqrt{5} + \sqrt{3}}{ \sqrt{5} + \sqrt{3}} \\= \frac{ (\sqrt{5} + \sqrt{3})^{2} }{ (\sqrt{5})^2 - (\sqrt{3})^2} \\= \frac{5 + 3 + 2\sqrt{5} \sqrt{3}}{5 - 3} \\= \frac{8 + 2\sqrt{5} \sqrt{3}}{2}$