Question

Find the value of $\frac{\sqrt{12}}{5\sqrt{6}+\sqrt{24}-\sqrt{54}}$

• A. $\frac{1}{4}\sqrt{2}$
  
• B. $\frac{2}{2\sqrt{2}}$
• C. $\frac{1}{4\sqrt{2}}$
• D. $\frac{1}{2\sqrt{4}}$

Answer 1

The correct option is A $\frac{1}{4}\sqrt{2}$


$\frac{\sqrt{12}}{5\sqrt{6}+\sqrt{24}-\sqrt{54}}$

We know that,

$\sqrt{24}=\sqrt{4\times 6}=2\sqrt{6}$
$\sqrt{54}=\sqrt{9\times 6}=3\sqrt{6}$
Hence,
$\frac{\sqrt{12}}{5\sqrt{6}+\sqrt{24}-\sqrt{54}}$
$=\frac{\sqrt{12}}{5\sqrt{6}+2\sqrt{6}-3\sqrt{6}}$
$=\frac{\sqrt{2\times 6}}{7\sqrt{6}-3\sqrt{6}}$
$=\frac{\sqrt{2}\times \sqrt{6}}{4\sqrt{6}}$
$=\frac{1}{4}\sqrt{2}$