Question

Simplify the expression: $\frac{1}{\frac{\sqrt{66}}{\sqrt{2}\times \sqrt{3}}+\sqrt[4]{4144}}$

• A. $\sqrt{12}+\sqrt{11}$
• B. $\sqrt{12}-\sqrt{11}$

Answer 1

The correct option is B $\sqrt{12}-\sqrt{11}$

$\frac{1}{\frac{\sqrt{66}}{\sqrt{2}\times \sqrt{3}}+\sqrt[4]{4144}}$
$=\frac{1}{\sqrt{\frac{66}{2\times 3}}+\sqrt[4]{4{12}^2}}$
$=\frac{1}{\sqrt{11}+\sqrt{12}}$
$=\frac{1}{\sqrt{11}+\sqrt{12}}\times \frac{\sqrt{11}-\sqrt{12}}{\sqrt{11}-\sqrt{12}}$
$=\frac{\sqrt{11}-\sqrt{12}}{(\sqrt{11}{)}^2-(\sqrt{12}{)}^2}$
$=\frac{\sqrt{11}-\sqrt{12}}{11-12}$
$=\sqrt{12}-\sqrt{11}$