Aptitude Question ID: 107076

\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}} is equal to :
[A]1
[B]2
[C]3
[D]8

2
Given, \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}
= \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{4+3+2\times2\times\sqrt{3}}}}
= \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{(2)^{2}+(\sqrt{3})^{2}+2\times 2\times \sqrt{3}}}}
= \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{(2+\sqrt{3})^{2}}}}
= \sqrt{-\sqrt{3}+\sqrt{3+8(2+\sqrt{3})}}
= \sqrt{-\sqrt{3}+\sqrt{3+16+8\sqrt{3}}}
= \sqrt{-\sqrt{3}+\sqrt{(\sqrt{3})^{2}+(4)^{2}+2\times 4\times \sqrt{3}}}
= \sqrt{-\sqrt{3}+\sqrt{(4+\sqrt{3})^{2}}}
= \sqrt{-\sqrt{3}+4+\sqrt{3}} = \sqrt{4} = 2
Hence option [B] is correct answer.

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