Question

rationalise the denominator of the following :
$\frac{ \sqrt{11 - \sqrt{5} } }{ \sqrt{11 + \sqrt{5} } }$

Answer 1

According to given sum,

=> $\frac{ \sqrt{11 - \sqrt{5} } }{ \sqrt{11 + \sqrt{5} } }$

$= > \: \frac{ \sqrt{11 - \sqrt{5} } }{ \sqrt{11 + \sqrt{5} } } \times \frac{ \sqrt{11 - \sqrt{5} } }{ \sqrt{11 - \sqrt{5} } }$

$= > \: \frac{ \sqrt{ {(11 - \sqrt{5}) }^{2} } }{ \sqrt{ {11}^{2} - { \sqrt{5} }^{2} } }$

$= > \: \frac{11 - \sqrt{5} }{ \sqrt{121 - 5} }$

$= > \: \frac{11 - \sqrt{5} }{ \sqrt{116} }$

$= > \: \frac{11 - \sqrt{5} }{ \sqrt{116} } \times \frac{ \sqrt{116} }{ \sqrt{116} }$

$= > \: \frac{ \sqrt{116} (11 - \sqrt{5} )}{ {116} }$

:-)Hope it helps u.