SATHEE: Quantitative Aptitude Ques 1012

Quantitative Aptitude Ques 1012

Question: The value of $ \sqrt{\frac{(\sqrt{12}-\sqrt{8})(\sqrt{3}+\sqrt{2})}{5+\sqrt{24}}} $ is

Options:

A) $ \sqrt{6}-\sqrt{2} $

B) $ \sqrt{6}+\sqrt{2} $

C) $ \sqrt{6}-2 $

D) $ 2-\sqrt{6} $

Show Answer

Answer:

Correct Answer: C

Solution:

$ \sqrt{\frac{(12–\sqrt{8})(\sqrt{3}+\sqrt{2})}{5+\sqrt{24}}}=\sqrt{\frac{\sqrt{36}-\sqrt{24}+\sqrt{24}-\sqrt{16}}{5+\sqrt{24}}} $ $ =\sqrt{\frac{6-4}{5+\sqrt{24}}}=\sqrt{\frac{2}{5+2\sqrt{6}}} $ $ =\sqrt{\frac{(2)(5-2\sqrt{6})}{(5+2\sqrt{6})(5-2\sqrt{6})}}=\sqrt{\frac{2(5-2\sqrt{6})}{25-24}} $ $ =\sqrt{2(5-2\sqrt{6})} $ $ =\sqrt{2[{{(\sqrt{3})}^{2}}+{{(\sqrt{2})}^{2}}-2\sqrt{3}\sqrt{2})]} $ $ =\sqrt{2,{{(\sqrt{3}-\sqrt{2})}^{2}}} $ $ =\sqrt{2},(\sqrt{3}-\sqrt{2})=\sqrt{6}-2 $

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