Why can\'t the rational expressing $\\sqrt{x}$ be reducible?

Why can\'t the rational expressing $\\sqrt{x}$ be reducible? References I am missing an obvious fact here. Suppose there is a rational that satisfies $({p \\over q})^2$. All of the proofs I have read state this fraction has to be irreducible, that is, it has $gcd(p, q) = 1$. Why can\'t the rational be reducible?