Question

Rationalise the denominator of $\frac{1}{\sqrt{6}-\sqrt{5}-\sqrt{11}}$

• A. -$\frac{\sqrt{60}(\sqrt{6}+\sqrt{5}+\sqrt{11})}{60}$
• B. -$\frac{\sqrt{30}(\sqrt{6}+\sqrt{5}+\sqrt{11})}{60}$
• C. $\frac{\sqrt{3}(\sqrt{6}+\sqrt{5}+\sqrt{11})}{60}$
• D. $\frac{\sqrt{30}(\sqrt{6}+\sqrt{5}+\sqrt{11})}{60}$

Answer 1

Answer: (B)

-$\frac{\sqrt{30}(\sqrt{6}+\sqrt{5}+\sqrt{11})}{60}$

Co-factor of denominator $\sqrt{6}-\sqrt{5}-\sqrt{11}$ is $\sqrt{6}-\sqrt{5}+\sqrt{11}$.
Multiplying numerator and denominator with the co-factor,
$\frac{1}{\sqrt{6}-\sqrt{5}-\sqrt{11}}=\frac{1}{\sqrt{6}-\sqrt{5}-\sqrt{11}}\ast \frac{\sqrt{6}-\sqrt{5}+\sqrt{11}}{\sqrt{6}-\sqrt{5}+\sqrt{11}}$
$=\frac{\sqrt{6}-\sqrt{5}+\sqrt{11}}{(\sqrt{6}-\sqrt{5}{)}^2-11}=\frac{\sqrt{6}-\sqrt{5}+\sqrt{11}}{-2\sqrt{30}}$
Now multiplying numerator and denominator with $\sqrt{30}$,
$\frac{1}{\sqrt{6}-\sqrt{5}-\sqrt{11}}=\frac{-\sqrt{30}(\sqrt{6}-\sqrt{5}+\sqrt{11})}{60}$