| The simplified value of \[\sqrt{5+\sqrt{11+\sqrt{19\sqrt{28+\sqrt{64}}}}}\]is [SSC (CPO) 2009] |
A) 3
B) 2
C) 4
D) 6
Correct Answer: A
Solution :
(a) \[\sqrt{5+\sqrt{11+\sqrt{19+\sqrt{28+\sqrt{64}}}}}\] \[=\sqrt{5+\sqrt{11+\sqrt{19+\sqrt{28+8}}}}\] \[=\sqrt{5+\sqrt{11+\sqrt{19+\sqrt{36}}}}\] \[=\sqrt{5+\sqrt{11+\sqrt{19+6}}}\] \[=\sqrt{5+\sqrt{11+5}}=\sqrt{5+\sqrt{16}}\] \[=\sqrt{5+4}=\sqrt{9}=3\]
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