Question

Rationalise the denominator of:

1/root 6+root 5 -root 11

Answer 1

1/root 6 + root 5 - root 11 * 1/(root 6 + root 5) + root 11
root 6 + root 5 + root 11 / (root 6 + root 5)^2 - (root 11)^2
root 6 + root 5 + root 11 / 6+5+2 root 30 - 11
root 6 + root 5 + root 11 / 2 root 30
root 180 + root 150 + root 330 / 60  -----------------> ans

hope it helps

Answer 2

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