# Math Help - proof that cuberoot 2 is not rational

1. ## proof that cuberoot 2 is not rational

How would i prove that cuberoot 2 is not rational?

Let cuberoot 2 be written in the form m/n, where m and n are coprime.
So then $m^3=2n^3$
Hence $m^3$ and thus m is divisible by 2
So there exists integer k such that m=2k
thus $8k^3$ = $2n^3$
Thus $n^3$ = $4k^3$

Where do i go next? im stuck. Does it matter that its 4k^3 instead of say 2k^3? Can i just say that n^3 is thus even?

2. Can't you continue as in the proof about $\sqrt{2}$? Namely, $n^3=4k^3$ implies that n is even and so m and n and not coprime.

3. thanks! i got confused a bit because of the 4k^3 instead of a 2.