A) 1
B) 2
C) 3
D) 8
Correct Answer: D
Solution :
\[\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}\] \[=\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{4+3+2\times 2\times \sqrt{3}}}}\] \[=\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{{{(2)}^{2}}+{{(\sqrt{3})}^{2}}+2\times 2\times \sqrt{3}}}}\] \[=\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{{{(2+\sqrt{3})}^{2}}}}}\] \[=\sqrt{-\sqrt{3}+\sqrt{3+8(2+\sqrt{3})}}\] \[=\sqrt{-\sqrt{3}+\sqrt{3+16+8\sqrt{3}}}\] \[=\sqrt{-\sqrt{3}+\sqrt{{{(\sqrt{3})}^{2}}+{{(4)}^{2}}+2\times 4\times \sqrt{3}}}\] \[=\sqrt{-\sqrt{3}+{{(4+\sqrt{3})}^{2}}}\] \[=\sqrt{-\sqrt{3}+4+\sqrt{3}}=\sqrt{4}=2\]
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