Question

Simplify by combining similar terms: $3\sqrt{147}-\frac{7}{3}\sqrt{\frac{1}{3}}+7\sqrt{\frac{1}{3}}$.

Answer 1

We need to simplify $3\sqrt{147}-\frac{7}{3}\sqrt{\frac{1}{3}}+7\sqrt{\frac{1}{3}}$.

Here we can combine two similar terms by taking $\sqrt{\frac{1}{3}}$ common as,

$3\times 7\sqrt{3}-\sqrt{\frac{1}{3}}(\frac{7}{3}-7)$

$=21\sqrt{3}+\frac{14}{3}\sqrt{\frac{1}{3}}$

$=\frac{(63\times 3+14)}{3\sqrt{3}}$

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