Question:
Find the value of $\frac{21 \sqrt{12}}{10 \sqrt{27}}$.
Solution:
$\frac{21 \sqrt{12}}{10 \sqrt{27}}=\frac{21 \sqrt{2 \times 2 \times 3}}{10 \sqrt{3 \times 3 \times 3}}$
$=\frac{21 \times 2 \sqrt{3}}{10 \times 3 \sqrt{3}}$
$=\frac{3 \times 7 \times 2}{5 \times 2 \times 3}$
$=\frac{7}{5}$
Hence, the value of $\frac{21 \sqrt{12}}{10 \sqrt{27}}$ is $\frac{7}{5}$.
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