Question

rationalise the denominator of root 6 -root 5 ÷ root 6 +root 5​

Answer 1

Step-by-step explanation:

$\frac{ \sqrt{6 } - \sqrt{5} }{ \sqrt{6} + \sqrt{5} }$

$= \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} - \sqrt{5} }$

$= \frac{( \sqrt{6} - \sqrt{5} ) {}^{2} }{6 - 5}$

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

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

$= 11 - 2 \sqrt{30}$