The claim is that the square root of a prime number is irrational. This is a proof with flavors all over the Internet, but mine seems a teensy bit simpler than most, so I assume something is wrong with it

Assume sqrt (p) is in Q. so sqrt (p) = m/n for some relatively prime m,n in Z. squaring both sides, p= m^2 / n^2 or n*n*p = m*m. m divides n*n*p, but m and n have no common factors, so n must be 1 and m divides p. But p was prime, so contradiction and sqrt p is irrational.