Is the square root of 6 a rational or irrational number

So let's assume that the square root of 6 is rational. By definition, that means there are two integers a and b with no common divisors where: a/b = square root of 6. But this last statement means the RHS (right hand side) is even, because it is a product of integers and one of those integers (at least) is even.

Let's assume that it's rational: 

Then  hence  is even, which can be written 

Hence  thus 

Thus p,q are both even, which is absurd.

Hence sqrt(6) is irrational