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