Question

Simplify by combining similar terms in the following.

$3\sqrt{147}-\frac{7}{3}\sqrt{\frac{1}{3}}+7\sqrt{\frac{1}{3}}$

Answer 1

$3\sqrt{147}-\frac{7}{3}\sqrt{\frac{1}{3}}+7\sqrt{\frac{1}{3}}$
$=3\sqrt{49\times 3}+(\frac{-7}{3}+7)\sqrt{\frac{1}{3}}$
$=3\sqrt{49}\sqrt{3}+\frac{14}{3}.\frac{\sqrt{1}}{\sqrt{3}}$

$=3\sqrt{7^2}\sqrt{3}+\frac{14}{3}\sqrt{\frac{1}{3}}$
$\mathrm{3.7.}\sqrt{3}+\frac{14}{3}.\frac{\sqrt{1}}{\sqrt{3}}$

$=21\sqrt{3}+\frac{14}{3\sqrt{3}}$
$=21\sqrt{3}+\frac{14}{9}.\frac{\sqrt{3}}{\sqrt{3}}$

$=21\sqrt{3}+\frac{14}{3.3}\sqrt{3}$
$=21\sqrt{3}+\frac{14}{9}\sqrt{3}$

$=(\frac{21}{1}+\frac{14}{9})\sqrt{3}$
$=\frac{189+14}{9}\sqrt{3}$

$=\frac{203}{9}\sqrt{3}=\frac{203}{3\sqrt{3}}$