Question
Simplify : $5 \sqrt{3}+2 \sqrt{27}+\frac{1}{\sqrt{3}}$
✓
Answer
$\begin{aligned} & 5 \sqrt{3}+2 \sqrt{27}+\frac{1}{\sqrt{3}} \\ = & 5 \sqrt{3}+2 \sqrt{9 \times 3}+\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \\ = & 5 \sqrt{3}+2 \times 3 \sqrt{3}+\frac{\sqrt{3}}{3} \\ = & 5 \sqrt{3}+6 \sqrt{3}+\frac{\sqrt{3}}{3} \\ = & \left(5+6+\frac{1}{3}\right) \sqrt{3} \\ = & \left(11+\frac{1}{3}\right) \sqrt{3}=\left(\frac{33+1}{3}\right) \sqrt{3}=\frac{34}{3} \sqrt{3} \\ \therefore \quad & 5 \sqrt{3}+2 \sqrt{27}+\frac{1}{\sqrt{3}}=\frac{34}{3} \sqrt{3}\end{aligned}$
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