Question : The value of $\sqrt{–\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$ is:
Option 1: 2
Option 2: 4
Option 3: $\pm 2$
Option 4: –2
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Correct Answer: 2
Solution :
Given:
$\sqrt{–\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$
$=\sqrt{–\sqrt{3}+\sqrt{3+8\sqrt{(\sqrt{3})^{2}+2^{2}+2×2\sqrt{3}}}}$
$=\sqrt{–\sqrt{3}+\sqrt{3+8\sqrt{{3}}+16}}$
$=\sqrt{–\sqrt{3}+\sqrt{(\sqrt{3})^{2}+4^{2}+2×4×\sqrt{3}}}$
$=\sqrt{–\sqrt{3}+\sqrt{3}+4}$
$=\sqrt{4}$
$ =2$
Hence, the correct answer is 2.
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