Complex number 3

$\large\sqrt{-2} \times\ \sqrt{-1}$

$\large=\sqrt{2} \sqrt{-1} \times\ \sqrt{-1}$

$\large=\sqrt{2} \times\ i \times\ i$

$\large=\sqrt{2} \times\ i^2$

$\large= -\sqrt{2}$

$\sqrt{-2} \times \sqrt{-1}$

$= \sqrt{-1} \sqrt{2} \times i$

$= \sqrt{2} i^2$

$= \sqrt{2}(-1)$

$= \boxed{-\sqrt 2}$

$\sqrt{-2} (\sqrt{-1}) = i\sqrt{2}(i\sqrt{1})=i\sqrt{2}(i)=i^2\sqrt{2}=-\sqrt{2}$

Here, $\sqrt{a} \times \sqrt{b}$ , where $a$ and $b$ are negative, is not equal to $\sqrt{ab}$ ! $\begin{aligned} \sqrt{-2} \times \sqrt{-1} &= i\sqrt{2} \times i \\ &= i^2\sqrt{2} \\ &= \boxed{-\sqrt{2}} \end{aligned}$

Therefore, the answer is $-\sqrt{2}$ .