Find the curvature of the generating curve.

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Homework Statement


A surface is formed by revolving y=x^(8/5) / 4 between [0,5] about the y-axis. Find the curvature of the generating curve. Graph the function of the generating curve.

This is a question from a mathematica project. The book we are using is Stewart Multivariable Calculus 6E. I can't seem to find "generating curves" in the index of the book, so I am clueless where to look for help.
 
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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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