What is the smallest number by which, 9720 should be divided to get a perfect cube?

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answer is C.

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Detailed Solution

It is required to find the smallest number by which, 9720 should be divided to get a perfect cube.
Utilizing prime factorization, express the given number as a product of the factors in the triple form.

⇒ 9720 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5 ⇒ 23 × 33 × 45

The number 9720 is not a perfect cube because the numbers 3 and 5 do not have triples. As of right now, if we divide 9720 by 45, the result is a perfect cube.
To create a perfect cube, 9720 must be divided by the fewest possible number 45.
Therefore, option 3 is correct.

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