Question

Rationalize pls help

Answer 1

Question :

$\tt Rationalize \: \frac{1}{\sqrt{5} - \sqrt{3}}$

Concepts :

To rationalize the denominator we have to multiply by its conjugate.

Solution :

$\tt \frac{1}{\sqrt{5} - \sqrt{3}}$

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

$\tt \implies \frac{\sqrt{5}+\sqrt{3}}{{(\sqrt{5})}^{2} - {(\sqrt{3})}^{2}}$

$\tt \implies \frac{\sqrt{5}+\sqrt{3}}{5-3}$

$\tt \implies \frac{\sqrt{5}+\sqrt{3}}{2}$

Hence denominator is rationalized.

Answer 2

Answer:

Question :

$\tt Rationalize \: \dfrac{1}{\sqrt{5} - \sqrt{3}}$

Concepts :

To rationalize the denominator we have to multiply by its conjugate.

Solution :

$\tt \dfrac{1}{\sqrt{5} - \sqrt{3}}$

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

$\tt \implies \dfrac{\sqrt{5}+\sqrt{3}}{{(\sqrt{5})}^{2} - {(\sqrt{3})}^{2}}$

$\tt \implies \dfrac{\sqrt{5}+\sqrt{3}}{5-3}$

$\tt \implies \dfrac{\sqrt{5}+\sqrt{3}}{2}$

Hence denominator is rationalized.