Square root of 3 is irrational

[Thecla]

I am trying to prove sqrt(3) is irrational. I figured I would do it the same way that sqrt(2) is irrational is proved:
Assume sqrt(2)=p/q
You square both sides.
and you get p^2 is even, therefore p is even.
Also q^2 is shown to be even along with q.
This leads to a contradiction.
However doing this with sqrt(3), you get 3q^2=p^2. Now you can't show p^2 is even.Also now I am stuck. How do I continue from here?

 

[jacobrhcp]

So maybe when going from 2 to 3, you don't need to use evenness but 'divisible by three' ;)

 

[Thecla]

Thanks jacobrhcp. If p^2 =3q^2, then p must be a multiple of 3. The same goes for q^2 and q, both are multiples of 3.