Question

rationalise the denominator of 1/√5+√3 with steps

​

Answer 1

$\frac{\sqrt{5}-\sqrt{3}}{2}$

Step-by-step explanation:

$\frac{1}{\sqrt{5}+\sqrt{3}}$

$= \frac{1}{\sqrt{5}+\sqrt{3}} \times \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

$= \frac{1(\sqrt{5}-\sqrt{3})}{(\sqrt{5-}+\sqrt{3})(\sqrt{5}-\sqrt{3})}$

$\mathrm{\because (a +b)(a-b) = a^2 - b^2}$

$\therefore \frac{\sqrt{5}-\sqrt{3}}{5-3}$

$= \frac{\sqrt{5}-\sqrt{3}}{2}$