Question

The value of $\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$ is

• A. $2$
• B. $4$
• C. $\pm 2$
• D. $-2$

Answer 1

Answer: (C)

The correct option is C $\pm 2$
$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$
$=\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{(\sqrt{3}{)}^2+2^2+2\times 2\sqrt{3}}}}$
$=\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{3}+16}}$
$=\sqrt{-\sqrt{3}+\sqrt{(\sqrt{3}{)}^2+4^2+2\times 4\times \sqrt{3}}}$
$=\sqrt{-\sqrt{3}+\sqrt{3}+4}=\sqrt{4}=\pm 2$.