Rationalize frac 2 sqrt 3 sqrt 5 sqrt 5 - sqrt 3 - JAMB Physics 2010 Question
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 option: d
\(\frac{2\sqrt{3}} + \sqrt{5}}{\sqrt{5} - \sqrt{3}\) = \(\frac{\sqrt{5}} + 2\sqrt{3}}{\sqrt{5} - \sqrt{3}\) x \(\frac{\sqrt{5}} + \sqrt{3}}{\sqrt{5} + \sqrt{3}\)
\(\frac{5 + \sqrt{15} + 2\sqrt{15} + 2 \times 3}{(\sqrt{5} - \sqrt{3})^2\)
= \(\frac{5 + 3\sqrt{15} +6} {5 - 3)\)
= \(\frac{11 + 3\sqrt{15}}{2}\)
\(\frac{5 + \sqrt{15} + 2\sqrt{15} + 2 \times 3}{(\sqrt{5} - \sqrt{3})^2\)
= \(\frac{5 + 3\sqrt{15} +6} {5 - 3)\)
= \(\frac{11 + 3\sqrt{15}}{2}\)
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