Question

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

• A. 4.48
• B. 4.49
• C. 4.5
• D. None of these

Answer 1

The correct option is D None of these

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

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

$=\frac{\sqrt{6}}{3}+\frac{3\sqrt{6}}{2}=\frac{2.55}{3}+\frac{3\times 2.55}{2}$

$=\frac{2.55}{3}+\frac{7.65}{2}=\frac{5.10+22.95}{6}$

$=\frac{28.05}{6}=4.675$