Question

The value of $\frac{4\sqrt{12}}{12\sqrt{27}}$ is
(a) $\frac{1}{9}$

(b) $\frac{2}{9}$

(c) $\frac{4}{9}$

(d) $\frac{8}{9}$

Answer 1

$$\begin{gathered} \frac{4\sqrt{12}}{12\sqrt{27}} \\ =\frac{4\sqrt{2\times 2\times 3}}{12\sqrt{3\times 3\times 3}} \\ =\frac{4\times 2\sqrt{3}}{12\times 3\sqrt{3}} \\ =\frac{2}{9} \end{gathered}$$
Hence, the correct answer is option (b).