Question : What is the value of $\sqrt{4600+\sqrt{540+\sqrt{1280+\sqrt{250+\sqrt{36}}}}}$?
Option 1: 69
Option 2: 68
Option 3: 70
Option 4: 72
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Correct Answer: 68
Solution :
Given: $\sqrt{4600+\sqrt{540+\sqrt{1280+\sqrt{250+\sqrt{36}}}}}$
$\sqrt{4600+\sqrt{540+\sqrt{1280+\sqrt{250+\sqrt{6^2}}}}}$
$=\sqrt{4600+\sqrt{540+\sqrt{1280+\sqrt{256}}}}$
$=\sqrt{4600+\sqrt{540+\sqrt{1280+\sqrt{16^2}}}}$
$=\sqrt{4600+\sqrt{540+\sqrt{1296}}}$
$=\sqrt{4600+\sqrt{540+\sqrt{36^2}}}$
$=\sqrt{4600+\sqrt{576}}$
$=\sqrt{4600+\sqrt{24^2}}$
$=\sqrt{4624}$
$=\sqrt{68^2}$
$=68$
Hence, the correct answer is 68.
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