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) $\frac{8}{9}$
Solution:
$\frac{4 \sqrt{12}}{12 \sqrt{27}}$
$=\frac{4 \sqrt{2 \times 2 \times 3}}{12 \sqrt{3 \times 3 \times 3}}$
$=\frac{4 \times 2 \sqrt{3}}{12 \times 3 \sqrt{3}}$
$=\frac{2}{9}$
Hence, the correct answer is option (b).
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