Question

The value of $\frac{9}{\sqrt{11}+\sqrt{2}}$ is equal to

• A. $9(\sqrt{11}+\sqrt{2})$
• B. $9(\sqrt{11}-\sqrt{2})$
• C. $\sqrt{11}-\sqrt{2}$
• D. $\frac{9}{(\sqrt{11}-\sqrt{2})}$

Answer 1

The correct option is C $\sqrt{11}-\sqrt{2}$

$\frac{9}{\sqrt{11}+\sqrt{2}}=\frac{9}{\sqrt{11}+\sqrt{2}}\times \frac{\sqrt{11}-\sqrt{2}}{\sqrt{11}-\sqrt{2}}$ ..... [By rationalizing]

$=\frac{9(\sqrt{11}-\sqrt{2})}{11-2}$

$=\frac{9(\sqrt{11}-\sqrt{2})}{9}=\sqrt{11}-\sqrt{2}$