Question

Rationalisie the denominator of: 2/√7+√5​

Answer 1

Answer:

$\longmapsto \sqrt{7} - \sqrt{5} .$

Step-by-step explanation:

$\sf{\:\dfrac{2}{\sqrt{7} + \sqrt{5}}}$

By rationalizing the denominator,

$=\sf{\dfrac{2}{\sqrt{7} + \sqrt{5}}\times \dfrac{\sqrt{7} - \sqrt{5}}{\sqrt{7} - \sqrt{5}}}$

$=\sf{\dfrac{2(\sqrt{7} - \sqrt{5})}{(\sqrt{7} + \sqrt{5})(\sqrt{7} - \sqrt{5})}}$

$=\sf{\dfrac{2(\sqrt{7} - \sqrt{5})}{(\sqrt{7})^2 - (\sqrt{5})^2}}$

$=\sf{\dfrac{2(\sqrt{7} - \sqrt{5})}{7 - 5}}$

$=\sf{\dfrac{2(\sqrt{7} - \sqrt{5})}{2}}$

$=\sf{\dfrac{\not{2}(\sqrt{7} - \sqrt{5})}{\not{2}}}$

$\boxed{\underline{\rm{\therefore\:\dfrac{2}{\sqrt{7} + \sqrt{5}} = \sqrt{7} - \sqrt{5}}}}$