(-2 ) (-3 ) is equal to: - Vidyadip

MCQ

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

A
$\sqrt{6}$
B
$-\sqrt{6}$
C
$\text{i}\sqrt{6}$
D
none of these.

✓

Answer

$-\sqrt{6}$

Solution:

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

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

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

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

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

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