Rationalize \( \frac{2\sqrt{3}} + \sqrt{5} \sqrt{5} - \sqrt{3} \)
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Correct Answer: Option D
Explanation:
\(\frac{2\sqrt{3}} + \sqrt{5}}{\sqrt{5} - \sqrt{3}\) = \(\frac{\sqrt{5}} + 2\sqrt{3}}{\sqrt{5} - \sqrt{3}\) x \(\frac{\sqrt{5}} + \sqrt{3}}{\sqrt{5} + \sqrt{3}\)
\(\frac{5 + \sqrt{15} + 2\sqrt{15} + 2 \times 3}{(\sqrt{5} - \sqrt{3})^2\)
= \(\frac{5 + 3\sqrt{15} +6} {5 - 3)\)
= \(\frac{11 + 3\sqrt{15}}{2}\)
\(\frac{2\sqrt{3}} + \sqrt{5}}{\sqrt{5} - \sqrt{3}\) = \(\frac{\sqrt{5}} + 2\sqrt{3}}{\sqrt{5} - \sqrt{3}\) x \(\frac{\sqrt{5}} + \sqrt{3}}{\sqrt{5} + \sqrt{3}\)
\(\frac{5 + \sqrt{15} + 2\sqrt{15} + 2 \times 3}{(\sqrt{5} - \sqrt{3})^2\)
= \(\frac{5 + 3\sqrt{15} +6} {5 - 3)\)
= \(\frac{11 + 3\sqrt{15}}{2}\)