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# help

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If $$x=720$$ and $$ax$$ is a perfect cube where $$a$$ is a positive integer, what is the smallest possible value of $$\sqrt[3]{ax}$$?

Jan 3, 2019

#1
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Factor 720.....

72 * 10

8 * 9 * 5 *2

2^3 * 3^2 * 5^1 * 2^1

To have a perfect cube......we need "a" to be   3 * 5^2 * 2^2  =  300

So....the smallest value is

∛ [  720 * 300 ]   =   ∛ [216000]   =   60

Jan 3, 2019