Find the smallest non-zero whole number n such that 756n is a perfect cube.

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Find the smallest non-zero whole number n such that 756n is a perfect cube.

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Doris 3 years 2021-08-23T05:03:44+00:00 1 Answers 8 views 0

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  1. Nem
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    2021-08-23T05:04:49+00:00
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    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.

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