# Prove that 5^(2/3) is irrational

1. Oct 10, 2012

### P-Illiterate

1. The problem statement, all variables and given/known data
Prove that 5^(2/3) is irrational

2. Relevant equations

3. The attempt at a solution

I tried writing a proof but that is not getting me any where.

This is what I did so far -

Show that 52/3 is irrational

Proof: Suppose that 52/3 is rational:
52/3 = a/b
52/33/2 = a3/2/b3/2
5(b3/2) = a3/2
Substitute a = 2n + 1, b = 2m + 1;

I don't know if I'm suppose to do like this?

2. Oct 10, 2012

### Staff: Mentor

It might be simpler to use the fact that 52/3 = $\sqrt[3]{25}$

3. Oct 10, 2012

### P-Illiterate

Gracias

4. Oct 10, 2012