Question

Rationalisie the denominator of: 3/√5+√2​

Answer 1

Answer:

$\longmapsto \: \sqrt{5} - \sqrt{2.}$

Step-by-step explanation:

$\sf{\dfrac{3}{\sqrt{5} + \sqrt{2}}}$

By rationalizing the denominator,

$=\sf{\dfrac{3}{\sqrt{5} + \sqrt{2}} \times \dfrac{\sqrt{5} - \sqrt{2}}{\sqrt{5} - \sqrt{2}}}$

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

Applying the identity in the denominator:-

$\boxed{\underline{\red{\rm{(a + b)(a - b) = a^2 - b^2}}}}$

$=\sf{\dfrac{3(\sqrt{5} - \sqrt{2})}{(\sqrt{5})^2 - (\sqrt{2})^2}}$

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

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

$=\sf{\dfrac{\not{3}(\sqrt{5} - \sqrt{2})}{\not{3}}}$

$\blue{\boxed{\underline{\rm{\therefore\:\dfrac{3}{\sqrt{5} + \sqrt{2}} = \sqrt{5} - \sqrt{2}}}}}$