Question

Simplify :

$\sqrt{216}-5\sqrt{6}+\sqrt{294}-\frac{3}{\sqrt{6}}$.

• A. $\left(\frac{5}{2}\right)\sqrt{6}$
• B. $\left(\frac{15}{2}\right)\sqrt{6}$
• C. $\left(\frac{10}{2}\right)\sqrt{6}$
• D. $\left(\frac{15}{3}\right)\sqrt{6}$

Answer 1

Answer: (B)

$\left(\frac{15}{2}\right)\sqrt{6}$

$\sqrt{216}-5\sqrt{6}+\sqrt{294}-\frac{3}{\sqrt{6}}$
$=6\sqrt{6}-5\sqrt{6}+7\sqrt{6}-\frac{3}{\sqrt{6}}$
$=8\sqrt{6}-\frac{3}{\sqrt{6}}$ $=\frac{8\times 6-3}{\sqrt{6}}$
$=\frac{45}{\sqrt{6}}$ $=\frac{45\times \sqrt{6}}{\sqrt{6}\times \sqrt{6}}$
$=\frac{45\sqrt{6}}{6}$ $=\frac{15\sqrt{6}}{2}$.

Therefore, option $B$ is correct.