Question

rationalise the denominator

Answer 1

$\frac{1}{ \sqrt{6} + \sqrt{5} - \sqrt{11} } \\ = \frac{( \sqrt{6} + \sqrt{5} ) + \sqrt{11} }{(( \sqrt{6} + \sqrt{5}) - \sqrt{11} ))(( \sqrt{6} + \sqrt{5}) + \sqrt{11} ) } \\ = \frac{ \sqrt{6} + \sqrt{5} + \sqrt{11} }{(( { \sqrt{6} + \sqrt{5} ) }^{2} - ( { \sqrt{11}) }^{2} } \\ = \frac{ \sqrt{6} + \sqrt{5} + \sqrt{11} }{6 + 5 + 2 \sqrt{30} - 11} \\ = \frac{ \sqrt{6} + \sqrt{5} + \sqrt{11} }{11 + 2 \sqrt{30} - 11} \\ = \frac{( \sqrt{6} + \sqrt{5} + \sqrt{11}) \sqrt{30} }{2 \sqrt{30} \times \sqrt{30} } \\ = \frac{( \sqrt{6} + \sqrt{5} + \sqrt{11}) \sqrt{30} }{2 \times 30} \\ = \frac{( \sqrt{6} + \sqrt{5} + \sqrt{11} ) \sqrt{30} }{60}$