Quantitative Aptitude Ques 1110

Question: Value of $ \sqrt{-\sqrt{5}+\sqrt{1+4\sqrt{9+4\sqrt{5}}}} $ is

Options:

A) $ \sqrt{2} $

B) $ \sqrt{3} $

C) $ 2 $

D) $ \sqrt{5} $

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ \sqrt{-\sqrt{5}\sqrt{1+4\sqrt{9+4\sqrt{5}}}} $ $ =\sqrt{-\sqrt{5}+\sqrt{1+4\sqrt{{{(2)}^{2}}+{{(\sqrt{5})}^{2}}+2\times 2\sqrt{5}}}} $ $ =\sqrt{-\sqrt{5}+\sqrt{1+4\sqrt{{{(2+\sqrt{5})}^{2}}}}} $ $ =\sqrt{-\sqrt{5}+\sqrt{1+4,(2+\sqrt{5})}} $ $ =\sqrt{-\sqrt{5}+\sqrt{9+4\sqrt{5}}} $ $ =\sqrt{-\sqrt{5}+(2+\sqrt{5})}=\sqrt{2} $
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