Intermediate Value Theorem proof

1. Oct 13, 2005

Anisotropic Galaxy

Prove that every nonnegative real number x has a unique nonnegative nth root x^(1/n).

The problem gives a hint - existence of x^(1/n) can be seen by applying intermediate value theorem to function f(t) = t^n for t>= 0.

But I still don't get it - proofs are such a hurdle for me. i'm hoping that I can get over that hurdle...soon...

Thanks!

2. Oct 13, 2005

ComputerGeek

try to get a contradiction of the statement you want to prove. so, assume that there exists two non negative real which have the same root. then you should be able to use the IVT to show that the two real numbers are actually the same number and that is a contradiction of your assumption which proves the proof statement.