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Cube Root Using Prime Factorisation

If the differ...

Question

If the difference between the smallest five digit perfect cube and the greatest four digit perfect cube is a then(a - 56) can be a cube of

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Solution

Smallest 5 digit perfect cube
22x22x22= 10648

Greatest 4 digit cube
21x21x21= 9261

Difference = 10648-9261
= 1387
a= 1387
Then,
1387-56= 1331 (which is cube of 11)
Therefore 11 is the correct answer

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