| Value of \[\sqrt{-\sqrt{5}+\sqrt{1+4\sqrt{9+4\sqrt{5}}}}\]is |
A) \[\sqrt{2}\]
B) \[\sqrt{3}\]
C) \[2\]
D) \[\sqrt{5}\]
Correct Answer: A
Solution :
| \[\sqrt{-\,\,\sqrt{5}\sqrt{1+4\sqrt{9+4\sqrt{5}}}}\] |
| \[=\sqrt{-\,\,\sqrt{5}+\sqrt{1+4\sqrt{{{(2)}^{2}}+{{(\sqrt{5})}^{2}}+2\times 2\sqrt{5}}}}\] |
| \[=\sqrt{-\,\,\sqrt{5}+\sqrt{1+4\sqrt{{{(2+\sqrt{5})}^{2}}}}}\] |
| \[=\sqrt{-\,\,\sqrt{5}+\sqrt{1+4\,(2+\sqrt{5})}}\] |
| \[=\sqrt{-\,\,\sqrt{5}+\sqrt{9+4\sqrt{5}}}\] |
| \[=\sqrt{-\,\,\sqrt{5}+(2+\sqrt{5})}=\sqrt{2}\] |
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