SOLUTION: Find the smallest number that can be subtracted from 9761 so that the difference is a perfect cube, and find the cube root of the difference.

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Question 701749: Find the smallest number that can be subtracted from 9761 so that the difference is a perfect cube, and find the cube root of the difference.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The largest perfect cube less than 9761 will differ from 9761
by a smaller amount than any smaller perfect cube will differ 
from it.

So we take the cube root of 9761.

∛9761 = 21.37132445

The largest integer less than that is 21.

So 21³ or 9261 is the largest perfect cube that's less that 9761.
And its difference from 9761 is 500.

So 500 is the smallest number that can be subtracted from 9761 
so that the difference, 9261, is a perfect cube --  and the cube
root of that difference is 21.

 Edwin