Griffiths Page 146: Understanding Binomial Expansion

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[SOLVED] Griffiths page 146

Homework Statement


EDIT: sorry I realized I posted this in the wrong forum; someone can move it to the advanced physics forum if you want

Please stop reading unless you have Griffiths E and M book.

On that page, Griffiths says "and then the binomial expansion yields" and I am not sure what binomial expansion he is talking about. On the next line how did he get the second approximate equality? How in the world did he get rid of the ( )^(-1/2) operation ?

Homework Equations


The Attempt at a Solution

 
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Never mind. See equation 3.93.
 
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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