Question

Rationalise the denominator
$\frac{2}{ \sqrt{5} - \sqrt{3} }$
​

Answer 1

Answer:

(√5 + √3)

Step-by-step-explanation:

Given:-

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

To rationalise the denominator, the numerator and denominator are multiplied by the conjugate.

Here's how that's carried out:-

$\bf \dfrac{2 \times \red{(\sqrt{5}+ \sqrt{3})}}{\sqrt{5} - \sqrt{3} \times \red{(\sqrt{5}+ \sqrt{3})}}$

$\sf \implies \dfrac{[2(\sqrt{5} + 2 \sqrt{3}]}{5-3}$

$\sf \implies \dfrac{2 (\sqrt{5} + \sqrt{3})}{2}$

$\implies \sf ( \sqrt{5} + \sqrt{3})$