Question

If $\sqrt{6}=2.55,$ then the value of $\sqrt{\frac{2}{3}}+3\sqrt{\frac{3}{2}}$ is

• A. $4.48$
• B. $4.49$
• C. $4.5$
• D. $4.675$

Answer 1

The correct option is B $4.49$

$\sqrt{\frac{2}{3}}+3\sqrt{\frac{3}{2}}$

$\Rightarrow \frac{\sqrt{2}\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}+3\times \frac{\sqrt{3}\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}$

$\Rightarrow \frac{\sqrt{6}}{3}+\frac{3\sqrt{6}}{2}$

$\Rightarrow \frac{2\sqrt{6}+9\sqrt{6}}{6}$

$\Rightarrow \frac{11\sqrt{6}}{6}$

Given $\sqrt{6}=2.45$

$\Rightarrow \frac{11\times 2.45}{6}=\frac{26.95}{6}=4.491$