Dimensions of box that minimize the material used

Winzer
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Homework Statement


A box with a square base and open top must have a volume of 32,000cm^3. Find the dimensions of the box that minimize the amont of material used.

Homework Equations


Sa(surface area)=4xy+x^2
Volume=x^2y

The Attempt at a Solution


I want to minimize Sa I am pretty sure so how do i begin?
 
Last edited:
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Never mind I figured it out.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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