The square root of 2 is not rational

Proof by contradiction

Let's assume that there exists a rational number q equal to 2. Therefore, by definition,

aN,bN{0},2=q=ab

We can also write it as an irreducible fraction, so that q=c/d, such that d does not divide c. From the properties of the square root, we have

q2=c2d2=2

We can multiply both sides by b2 to obtain

c2=2d2