Originally Posted by
SterlingM The problem is to proove that the square root of 5 is irrational via contradiction. I have gotten this far -
1.5^(1/2) is rational
2. 5^(1/2) = (a/b), a,b are coprime integers
3. 5 = (a^2/b^2)
4. 5b^2 = a^2
5. a^2 mod 5 = 0
6. a^2 = 5k, k is an integer
From here I don't know where to go. Honestly I'm not sure how I'm going to show a false statement. I understand the statements I have so far, but they are followed from a previous problem in my notes. The problem I have in my notes has this next step -
7. a^2 mod 5 = 0 -> a mod 5 = 0
Does this show a false statement? If so, I don't really see why. Can someone point me in the right direction? Thanks for any help.