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Solve: \( \Large \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} \)

A) \( \Large 4+\sqrt{15} \)
B) \( \Large 2+\sqrt{15} \)
C) \( \Large 2\sqrt{5}+2\sqrt{3} \)
D) \( \Large 4+2\sqrt{15} \)

Correct Answer:

A) \( \Large 4+\sqrt{15} \)

Description for Correct answer:
\( \Large \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} \)

multiply both Nr and Dr by \( \Large \sqrt{5}+\sqrt{3} \)

=\( \Large \frac{ \left(\sqrt{5}+\sqrt{3}\right) \left(\sqrt{5}+\sqrt{3}\right) }{ \left(\sqrt{5}+\sqrt{3}\right) \left(\sqrt{5}-\sqrt{3}\right) } = \frac{ \left(\sqrt{5}+\sqrt{3}\right)^{2} }{5-3} \)

= \( \Large \frac{ \left(\sqrt{5}\right)^{2}+ \left(\sqrt{3}\right)^{2}+2.\sqrt{5}.\sqrt{3} }{2} \)

= \( \Large \frac{5+3+2\sqrt{15}}{2} \)

=\( \Large \frac{8+2\sqrt{15}}{2}=4+\sqrt{15} \)

Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification

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