Question

$\sqrt{\sqrt{3}-\sqrt{4-\sqrt{5}-\sqrt{17-4\sqrt{15}}}}=$

• A. $0$
• B. $1$
• C. $\sqrt{3}$
• D. $\sqrt{2}$

Answer 1

The correct option is B $1$

$\sqrt{\sqrt{3}-\sqrt{4-\sqrt{5}-\sqrt{17-4\sqrt{15}}}}$

$\Rightarrow$ $\sqrt{\sqrt{3}-\sqrt{4-\sqrt{5}-\sqrt{12+5-2.\sqrt{12}.\sqrt{5}}}}$

$\Rightarrow$ $\sqrt{\sqrt{3}-\sqrt{4-\sqrt{5}-\sqrt{(\sqrt{12}-\sqrt{5}{)}^2}}}$

$\Rightarrow$ $\sqrt{\sqrt{3}-\sqrt{4-\sqrt{5}-\sqrt{12}+\sqrt{5}}}$

$\Rightarrow$ $\sqrt{\sqrt{3}-\sqrt{3+1-\mathrm{2.1.}\sqrt{3}}}$

$\Rightarrow$ $\sqrt{\sqrt{3}+1-\sqrt{3}}$

$\Rightarrow$ $\sqrt{1}$

$\Rightarrow$ $1$