Question

Rationalise the following denominator.​

Answer 1

$\frac{1}{ \sqrt{7 } \: + \sqrt{6} - \sqrt{13} }$

$= \frac{ \sqrt{7} + \sqrt{6} + \sqrt{13} }{( \sqrt{7} + \sqrt{6) {}^{2} } - 13 }$

$= \frac{ \sqrt{7} + \sqrt{6} + \sqrt{13} }{2 \sqrt{42} }$

$\frac{ \sqrt{7} + \sqrt{6} + \sqrt{13} }{2 \sqrt{42} } \times \frac{ \sqrt{42} }{ \sqrt{42} }$

$\frac{7 \sqrt{6} + 6 \sqrt{7} + \sqrt{546} }{84}$