Question

√2can be written as p/q so √2 is a rational numbers

Answer 1

Lets assume √2 is rational.

hence, √2 = p/q where p and q are coprime.

hence, 2q^2  = p^2

hence, p^2 is divisible by 2, and so is p.

therefore, let p = 2r (since p is even)

hence, 2q^2 = 4r^2

or, q^2 = 2r2

hence, even q is even.

let q = 2t

hence, √2 = 2r/2t

and there is a contradiction since p and q cannot have common factors.

Hence, √2 HAS to be irrational.