Question

State true or false:

$\sqrt{-2}.\sqrt{-3}=\sqrt{(-2)(-3)}=\sqrt{6}$.

For false type 0 and for true type 1

Answer 1

The computation $"\sqrt{-2}\sqrt{-3}=\sqrt{(-2)(-3)}=\sqrt{6}"$ is wrong since here both -2 and -3 are negative.
The correct computation is
$\sqrt{-2}\sqrt{-3}=\sqrt{2}\sqrt{-1}\sqrt{3}\sqrt{-1}=\sqrt{2}\sqrt{3}{\left(\sqrt{-1}\right)}^2$
$=\sqrt{6}(-1)=-\sqrt{6}.$