Simplify \(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}\)

Mathematics

WAEC 2005

A. \(\frac{1}{6}(5\sqrt{3}-3\sqrt{2}\)
B. \(\frac{1}{6}(15\sqrt{3}-6\sqrt{2}\)
C. \(\frac{1}{6}(3\sqrt{2}-\sqrt{3}\)
D. \(\frac{1}{6}(10\sqrt{3}-9\sqrt{2}\)

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Correct Answer: Option D

Explanation

\(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}}\\
=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}}Rationalize\\
\frac{\sqrt{6}(5\sqrt{2}-3\sqrt{3})}{6}\\
\frac{5\sqrt{12}-3\sqrt{18}}{6}=\frac{10\sqrt{3}-9\sqrt{2}}{6}\\
\frac{1}{6}(10\sqrt{3}-9\sqrt{2})\)

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