Math Help - Another Proof

1. Another Proof

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.

3. Originally Posted by dolphinlover
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?
You're on the right track.

Assume that $\sqrt{3} = \frac{a}{b}$ where a and be are integers and their ratio is irreducible.

You should find that both a and b have a factor of 3, and so their ratio is reducible.