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