At first I thought $\sqrt a\cdot\sqrt b$ is rational only when both $a$ and $b$ are squares of rational numbers. But then the example of $\sqrt2$ comes in and if $a=b=\sqrt2$, $\sqrt a\cdot\sqrt b$ is a rational number.
So what's the full version? Is $\sqrt a\cdot\sqrt b$ rational only when a and b are squares of rational numbers and $a=b$?
thanks!