Solving limit with squareroot -- how can i simplify

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Homework Statement



http://prntscr.com/cpbr3f

Homework Equations

The Attempt at a Solution


If I were to simply plug in 25 into the limit, i would get
((25)^(1/3) - 5)/25

Apparently the answer is 2/5. How the heck can you come to this conclusion?
 
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That would be the answer if that wasn't a cube root but a badly formatted ##3 \sqrt{t}##.
 
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Jonathan Scott said:
That would be the answer if that wasn't a cube root but a badly formatted ##3 \sqrt{t}##.
I think I'll proceed to slapping myself
 
Arnoldjavs3 said:
I think I'll proceed to slapping myself

No, don't slap yourself; slap the person who created the bad image.
 
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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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