Question

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

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

Answer 1

The correct option is C $\frac{34}{\sqrt{3}}$

Consider $5\sqrt{3}+2\sqrt{27}+\frac{1}{\sqrt{3}}$ and solve as follows:

$5\sqrt{3}+2\sqrt{27}+\frac{1}{\sqrt{3}}=5\sqrt{3}+(2\sqrt{3}\times \sqrt{{\left(3\right)}^2})+\frac{1}{\sqrt{3}}$

$=5\sqrt{3}+(2\sqrt{3}\times 3)+\frac{1}{\sqrt{3}}=5\sqrt{3}+6\sqrt{3}+\frac{1}{\sqrt{3}}=11\sqrt{3}+\frac{1}{\sqrt{3}}$

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

Hence, $5\sqrt{3}+2\sqrt{27}+\frac{1}{\sqrt{3}}=\frac{34}{\sqrt{3}}$.

Therefore, option $C$ is correct.