8 Powers
Level
pending
Find the positive square root of the smallest perfect square greater than
( \sqrt{11} + \sqrt{5} )^{8} + ( \sqrt{11} - \sqrt{5} )^{8}.
The answer is 951.
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1 solution
(11^(1/2)-5^(1/2))^8+(11^(1/2)+5^(1/2))^8 => 451856+60928 2^(1/2)+ 451856-60928 2^(1/2) => 903712
sqrt of 903712 is around 950.6(app.)
so the required answer lies between 950 and 951 but we are asked postive square root of perfect square therefor answer is 951 whose square is 904401 which is greater than 903172