Proof Writing & Problem Solving · Hard problem

A draft uses the inequality $\dfrac{a + b}{2} \ge \sqrt{ab}$ "for all real numbers $a$ and $b$ for which $\sqrt{ab}$ is defined" (that is, $ab \ge 0$). For how many ordered pairs $(a, b)$ of integers with $-3 \le a \le 3$ and $-3 \le b \le 3$ is $\sqrt{ab}$ defined but the inequality FALSE?