Question

Simplify $\frac{3}{\sqrt{5}+\sqrt{3}}$ by rationalising the denominator.

• A. $\frac{3(\sqrt{3}-\sqrt{5})}{2}$
• B. $\frac{3(\sqrt{5}-\sqrt{3})}{2}$
• C. $\frac{3(\sqrt{5}-\sqrt{3})}{8}$
• D. $\frac{3(\sqrt{5}-\sqrt{2})}{2}$

Answer 1

The correct option is B

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

The least rationalising factor of $\frac{3}{\sqrt{5}+\sqrt{3}}$ is $\sqrt{5}-\sqrt{3}$

So, multiplying and dividing by $\sqrt{5}-\sqrt{3}$, we get,

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

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

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