Show that the square root of three is not rational.
I've tried by assuming that it is rational and showing a contradiction...but I hit a wall...any suggestions?
Suppose sqrt(3) is rational. Then it has a unique factorization of prime numbers.
sqrt(3)=p1*p2*...*pn
sqrt(3)^2=3^1=p1^2*p2^2*...*pn^2
On left hand side exponent is odd and all exponents are even on right hand side.
By uniqueness of factorization of prime we have a contradiction. Thus sqrt(3) is not rational.