Question:
$(\sqrt{-2})(\sqrt{-3})$ is equal to
(a) $\sqrt{6}$
(b) $-\sqrt{6}$
(c) $i \sqrt{6}$
(d) none of these.
Solution:
(b) $-\sqrt{6}$
$\sqrt{-2} \times \sqrt{-3}$
$=\sqrt{2} \times \sqrt{3} \times \sqrt{-1} \times \sqrt{-1}$
$=\sqrt{6} \times i \times i$
$=\sqrt{6} \times i^{2}$
$=-\sqrt{6}$ $\left[\because i^{2}=-1\right]$