Question

rationalise the denominator √5-√6/√5+√6​

Answer 1

Answer:

$\frac{ \sqrt{5} - \sqrt{6} }{ \sqrt{5} + \sqrt{6} } = 11 + 2 \sqrt{30}$

Step-by-step explanation:

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