Question
Simplify : $2 \sqrt{48}-\sqrt{75}-\frac{1}{\sqrt{3}}$
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Answer
$\begin{aligned} & 2 \sqrt{48}-\sqrt{75}-\frac{1}{\sqrt{3}} \\ = & 2 \sqrt{16 \times 3}-\sqrt{25 \times 3}-\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \\ = & 2 \times 4 \sqrt{3}-5 \sqrt{3}-\frac{1}{3} \sqrt{3} \\ = & 8 \sqrt{3}-5 \sqrt{3}-\frac{1}{3} \sqrt{3} \\ = & \left(8-5-\frac{1}{3}\right) \sqrt{3} \\ = & \left(3-\frac{1}{3}\right) \sqrt{3} \\ = & \left(\frac{9-1}{3}\right) \sqrt{3} \\ = & \frac{8}{3} \sqrt{3} \\ \therefore \quad & 2 \sqrt{48}-\sqrt{75}-\frac{1}{\sqrt{3}}=\frac{8}{3} \sqrt{3}\end{aligned}$
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