Question

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

• A. $\frac{189}{3\sqrt{3}}$
• B. $\frac{175}{3\sqrt{3}}$
• C. $\frac{208\sqrt{3}}{3}$
• D. $\frac{203}{3\sqrt{3}}$

Answer 1

Answer: (D)

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

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

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

$=21\sqrt{3}+\sqrt{\frac{1}{3}}\left(\frac{21-7}{3}\right)$

$=21\times \frac{3}{\sqrt{3}}+\sqrt{\frac{1}{3}}\left(\frac{14}{3}\right)$

$=\frac{63}{\sqrt{3}}+\frac{14}{3\sqrt{3}}$

$=\frac{189+14}{3\sqrt{3}}$

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

So, $\text{D}$ is the correct option.