Proving Existence of x2=b for b≥0 in R

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Prove that if b is greater than or equal to zero (b in R), there exists a non-negative real number x such that x2=b.

I really don't know where to go. I think I need to modify a proof done in a class that I missed, so if someone could just give me a few hints I'll fill in the rest.

Thanks
Josh
 
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How have you defined the reals?

Or maybe prove that on [0, infinity), the function x -> x2 is continuous, increasing, and unbounded, and apply intermediate value theorem.
 
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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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