Aptitude Question ID: 107076

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

2
Given, $latex \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}&s=-1$
$latex = \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{4+3+2\times2\times\sqrt{3}}}}&s=-1$
$latex = \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{(2)^{2}+(\sqrt{3})^{2}+2\times 2\times \sqrt{3}}}}&s=-1$
$latex = \sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{(2+\sqrt{3})^{2}}}}&s=-1$
$latex = \sqrt{-\sqrt{3}+\sqrt{3+8(2+\sqrt{3})}}&s=-1$
$latex = \sqrt{-\sqrt{3}+\sqrt{3+16+8\sqrt{3}}}&s=-1$
$latex = \sqrt{-\sqrt{3}+\sqrt{(\sqrt{3})^{2}+(4)^{2}+2\times 4\times \sqrt{3}}}&s=-1$
$latex = \sqrt{-\sqrt{3}+\sqrt{(4+\sqrt{3})^{2}}}&s=-1$
$latex = \sqrt{-\sqrt{3}+4+\sqrt{3}} = \sqrt{4} = 2&s=-1$
Hence option [B] is correct answer.


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