Heres a proof I am getting stuck with

Prove sqrt(p) is irrational, p is set of all primes

so heres what Ihave

prove sqrt(p) is rational

sqrt(p) = a/b a,b set of integers, b not equal to 0, and a/b is in lowest form

p = a^2/b^2

p*b^2 = a^2.

a^2/p = b^2.

a/sqrt(P) = b

Kind of at a standstill here, since b cannot be rational when dividing by the sqrt of a prime. how can I say this?