Q44 / 160 · TS EAMCET 2007 · Mathematics
$\sqrt{2+\sqrt{5}-\sqrt{6-3 \sqrt{5}+\sqrt{14-6 \sqrt{5}}}}$ is equal to
- A$1$
- Correct answerB$2$
- C$3$
- D$4$
Solution
Now,
$\begin{aligned} \sqrt{2+} & \sqrt{5}-\sqrt{6-3 \sqrt{5}+\sqrt{14-6 \sqrt{5}}} \\ & =\sqrt{2+\sqrt{5}-\sqrt{6-3 \sqrt{5}+\sqrt{(9+5-6 \sqrt{5})}}} \\ & =\sqrt{2+\sqrt{5}-\sqrt{6-3 \sqrt{5}+\sqrt{(3-\sqrt{5})^2}}} \\ & =\sqrt{2+\sqrt{5}-\sqrt{9-4 \sqrt{5}}} \\ & =\sqrt{2+\sqrt{5}-\sqrt{(-2+\sqrt{5})^2}} \\ & =\sqrt{2+\sqrt{5}+2-\sqrt{5}} \\ & =2\end{aligned}$
Hence, the correct answer is option: 'B'.