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Question

Find the smallest number which when multiplied with 5184 will make the product a perfect cube.

A
2
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B
6
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C
3
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D
9
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Solution

The correct option is D 9
Write 5184 as a product of its primes.
25184225922129626482324216238132739 3

5184=(2×2×2)×(2×2×2)×(3×3×3)×3.

We find that in 5184 one ‘3’ is ungrouped. Thus, to convert 5184 to a perfect cube, we need to multiply it by 3×3=9.

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