Work out √(-16) × √(-25) correctly. Then work out √((-16) × (-25)).

Step 1. Each root first. $\sqrt{-16} = 4i$ and $\sqrt{-25} = 5i$.

Step 2. Multiply. $4i \times 5i = 20i^2 = -20$.

Step 3. Under one root. $(-16) \times (-25) = 400$, and $\sqrt{400} = 20$.

Step 4. Why they differ. The rule $\sqrt{a}\sqrt{b} = \sqrt{ab}$ was proved for $a, b \geq 0$. It does not hold when both are negative.