Question

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

Answer 1

$5\sqrt{3}+2\sqrt{27}+\frac{1}{\sqrt{3}}$
$=5\sqrt{3}+2\sqrt{9\times 3}+\frac{\sqrt{3}}{\sqrt{3}.\sqrt{3}}$
$=5\sqrt{3}+2\sqrt{9}\sqrt{3}+\frac{\sqrt{3}}{3}$

$=5\sqrt{3}+\mathrm{2.3.}\sqrt{3}+\frac{\sqrt{3}}{3}$
$=5\sqrt{3}+6\sqrt{3}+\frac{1}{3}.\sqrt{3}$

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

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