Question

find the smallest number that must be subtracted from 9761 so that the difference is a perfect cube

Answer 1

Hey Dear here is Your Answer =)

*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.

Hope it Helps You Out =)
Thanks (^^)

Pls Mark It as The BRAINLIEST...! (^_^)

Answer 2

∛9761 = 21.3713244481
The nearest number to 21.3713244481 is 21.
Therefore 
(21)³ = 9261.

The difference between 9761 and 9261 = 9761 - 9261
                                                                   = 500.

Therefore 500 is the smallest number which is to be subtracted from 9761 to make it a perfect cube.

Hope this helps you.