Find the smallest positive integer k such that 360k is a cube number.

Mathematics

2 answers:

MAXImum [283]3 years ago

8 0

Answer: k = 75

<u>Step-by-step explanation:</u>

360

∧

36 10

∧ ∧

6 6 2 5

∧ ∧

2 3 2 3

Prime factorization of 360 is: 2³ · 3² · 5

Since we want a perfect cube, every number must be to the power of 3.

That means we need a 3 and 2 more 5s to make a cube

k = 3 × 5 × 5

= 75

Luden [163]3 years ago

5 0

Answer:

k = 75

Step-by-step explanation:

Factorize 360

360 = 36 * 10

= 2 * 2 * 3 * 3 * 2 * 5

As 360k is cube number, k = 3 * 5 * 5

k = 75

360k = 360 * 75 = 27000 is a perfect cube

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Answer:

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