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If the product 46400k is a perfect fourth power, what is the smallest possible value of k?

 Jan 20, 2020
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46,400 =2^6 * 5^2 * 29^1. 

 

In order to make them all 4th powers, we have to add: 2^2 * 5^2 * 29^3 =2,438,900 - This is the smallest possible value of k. Because:2,438,900 * 46,400 =113,164,960,000^(1/4) =580 - perfect 4th power.

 Jan 20, 2020

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