$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$ 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.