>>12152660Not OP
Proof sqrt(2) is irrational.
1) Assume that 2 = (p/q)^2 where p/q is rational and in its lowest terms.
2) Then 2q^2=p^2 which means that p^2 is divisible by 2 and then also p is divisible by 2.
3) Set p=2m you have 2q^2=4m^2 which implies that q^2 is divisible by 2 which implies that q is divisible by 2 also.
4) Contradiction, then sqrt(2) is irrational.
This works always as long as you check that points 3,4 are legit for a given number. Iiirc if you try to prove that a rational sqrt is irrational with this method the proof breaks down at 3,4.
