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Find the smallest non-zero whole number n such that 756n is a perfect cube.
Question
Find the smallest non-zero whole number n such that 756n is a perfect cube.
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Mathematics
3 years
2021-08-23T05:03:44+00:00
2021-08-23T05:03:44+00:00 1 Answers
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Answers ( )
Step-by-step explanation:
756 = 2² * 3³ * 7.
For 756n to be a perfect cube, all of its prime factors must have a power that is a multiple of 3.
How to get from 2² to 2³: Multiply by 2.
3³ has already a power that is a multiple of 3.
How to get from 7 to 7³: Multiply by 7².
Hence n = 2 * 7² = 98.