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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

 

 

cool cool cool

 Jan 3, 2019

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