Question

Rationalise the denominator

$\frac{1}{ \sqrt{13} - \sqrt{5} }$

Answer 1

Hola Mate!!

Your answer :-

$= > \frac{1}{ \sqrt{13} - \sqrt{5} } \\ \\ = > \frac{1}{ \sqrt{13} - \sqrt{5} } \times \frac{ \sqrt{13} + \sqrt{5} }{ \sqrt{13} + \sqrt{5} } \\ \\ = > \frac{ \sqrt{13} + \sqrt{5} }{ {( \sqrt{13} )}^{2} - {( \sqrt{5}) }^{2} } \\ \\ = > \frac{ \sqrt{13} + \sqrt{5} }{13 - 5 } \\ \\ = > \frac{ \sqrt{13} + \sqrt{5} }{8}$

☆ Hope it helps ☆

Answer 2

hey!!

given :- 1/(√13-√5)

$= \frac{1}{ \sqrt{13} - \sqrt{5} } \times \frac{ \sqrt{13} + \sqrt{5} }{ \sqrt{13} + \sqrt{5} } \\ \\ = \frac{ \sqrt{13} + \sqrt{5} }{( \sqrt{13} - \sqrt{5} )( \sqrt{13} + \sqrt{5}) } \\ \\ = \frac{ \sqrt{13} + \sqrt{5} }{ ({ \sqrt{13} )}^{2} - {( \sqrt{5} )}^{2} } \\ \\ = \frac{ \sqrt{13} + \sqrt{5} }{13 - 5} \\ \\ = \frac{ \sqrt{13} + \sqrt{5} }{8}$

cheers!!!