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Square root of 3 is irrational

  1. Apr 29, 2012 #1
    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?
  2. jcsd
  3. Apr 29, 2012 #2
    So maybe when going from 2 to 3, you don't need to use evenness but 'divisible by three' ;)
  4. Apr 30, 2012 #3
    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.
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