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

## Homework Statement

Prove that 5^(2/3) is irrational

## 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?

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Mark44
Mentor

## Homework Statement

Prove that 5^(2/3) is irrational

## 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
52/3 3/2 = 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?
It might be simpler to use the fact that 52/3 = ##\sqrt[3]{25}##

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

Gracias

Mark44
Mentor