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Simplify: \( \Large \left[ \frac{\frac{3}{2+\sqrt{3}}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}} \right]\)

A) \( \Large \frac{1}{2}-5\sqrt{3} \)
B) \( \Large 2-5\sqrt{3} \)
C) 1
D) 0

Correct Answer:



C) 1

Description for Correct answer:
\( \Large \left[ \frac{\frac{3}{2+\sqrt{3}}-\frac{2}{2-\sqrt{3}}}{2-5\sqrt{3}} \right]\)

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

=\( \Large \frac{6-3\sqrt{3}-4-2\sqrt{3}}{ \left(2+\sqrt{3}\right) \left(2-\sqrt{3}\right) \left(2-5\sqrt{3}\right) }\)

=\( \Large \frac{2-5\sqrt{3}}{2-5\sqrt{3}} = 1 \)

Part of solved Indices and Surd questions and answers : >> Elementary Mathematics >> Indices and Surd

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Similar Questions

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D). \( \Large \sqrt[3]{4} \)

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A). \( \Large 5^{2} \)

B). \( \Large 5^{4} \)

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