This is the proof I used. Does anyone know if it is correct?
Assume that the sqrt(8) is a rational number.
sqrt(8) = n/m Assume no common factors between n and m
8 = n^2/m^2
8m^2 = n^2
So n^2 must be an even number since anything muliplied by 8 is even.
n must be even as well because even numbers squared are even, odd numbers squared are odd.
Represent n as 4k
n^2 = (4k)^2 --> 4^2k^2 --> 16k^2
8m^2 = 16k^2
m^2 = 2k^2
So, m^2 is even
So, m is even
Therefore m and n have a common factor, it disproves my assumption