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