Question

Simplify $4\sqrt{\frac{1}{3}}+\frac{1}{2}\sqrt{48}$

Answer 1

We have: $4\sqrt{\frac{1}{3}}+\frac{1}{2}\sqrt{48}=\frac{4}{\sqrt{3}}+\frac{\sqrt{48}}{2}=\frac{4}{\sqrt{3}}+\frac{4\sqrt{3}}{2}$ then the Rationalisation Factor of $\sqrt{3}$ is $\sqrt{3}$
$\therefore \frac{4}{\sqrt{3}}+\frac{4\sqrt{3}}{2}=\frac{4}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}+\frac{4\sqrt{3}}{2}=\frac{4\sqrt{3}}{3}+\frac{4\sqrt{3}}{2}$
$=\frac{8\sqrt{3}+12\sqrt{3}}{6}=\frac{20\sqrt{3}}{6}=\frac{10\sqrt{3}}{3}$
$\therefore 4\sqrt{\frac{1}{3}}+\frac{1}{2}\sqrt{48}=\frac{10\sqrt{3}}{3}$