Solve the following
Question:

$(\sqrt{-2})(\sqrt{-3})$ is equal to

(a) $\sqrt{6}$

(b) $-\sqrt{6}$

(c) $i \sqrt{6}$

(d) none of these.

Solution:

(b) $-\sqrt{6}$

$\sqrt{-2} \times \sqrt{-3}$

$=\sqrt{2} \times \sqrt{3} \times \sqrt{-1} \times \sqrt{-1}$

$=\sqrt{6} \times i \times i$

$=\sqrt{6} \times i^{2}$

$=-\sqrt{6}$ $\left[\because i^{2}=-1\right]$

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