Question

Rationalize the denominator 11/Square root of 5 - square root of 6

Answer 1

Answer:

$-11\sqrt{5}-11\sqrt{6}$

Step-by-step explanation:

The given radical expression is;

$\frac{11}{\sqrt{5}-\sqrt{6}}$

We multiply both the numerator and the denominator by the conjugate of

$\sqrt{5}-\sqrt{6}$ which is $\sqrt{5}+\sqrt{6}$

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

The denominator is now difference of two squares;

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

Simplify:

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

$\frac{11(\sqrt{5}+\sqrt{6})}{-1}$

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

$-11\sqrt{5}-11\sqrt{6}$