Simplify \(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}\)
- \(\frac{1}{6}(5\sqrt{3}-3\sqrt{2}\)
- \(\frac{1}{6}(15\sqrt{3}-6\sqrt{2}\)
- \(\frac{1}{6}(3\sqrt{2}-\sqrt{3}\)
-
\(\frac{1}{6}(10\sqrt{3}-9\sqrt{2}\)
The correct answer is: D
Explanation
\(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}}\\=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}}Rationalize\\
\frac{\sqrt{6}(5\sqrt{2}-3\sqrt{3})}{6}\\
\frac{5\sqrt{12}-3\sqrt{18}}{6}=\frac{10\sqrt{3}-9\sqrt{2}}{6}\\
\frac{1}{6}(10\sqrt{3}-9\sqrt{2})\)