Question

Simplify :

$5\sqrt{3}+2\sqrt{27}+\frac{1}{\sqrt{3}}$.

• A. $\frac{24\sqrt{3}}{3}$
• B. $\frac{34\sqrt{2}}{3}$
• C. $\frac{34\sqrt{3}}{2}$
• D. $\frac{34\sqrt{3}}{3}$

Answer 1

Answer: (D)

$\frac{34\sqrt{3}}{3}$

$5\sqrt{3}+2\sqrt{27}+\frac{1}{\sqrt{3}}$
$=5\sqrt{3}+(2\times 3)\sqrt{3}+\frac{1}{\sqrt{3}}$
$=11\sqrt{3}+\frac{1}{\sqrt{3}}$ $=\frac{(11\times 3)+1}{\sqrt{3}}$
$=\frac{33+1}{\sqrt{3}}$ $=\frac{34}{\sqrt{3}}$
$=\frac{34\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$ $=\frac{34\sqrt{3}}{3}$.

Therefore, option $D$ is correct.