Question

\(\Large \sqrt{-3}\sqrt{-2} \neq \sqrt{6}\)

Why?

Answer 1

because
\[\sqrt{a}\sqrt{b}=\sqrt{ab}\] only if \(a, b>0\)

Answer 2

But why? This is my question.

Answer 3

if you allow negative numbers under the radical, i.e. if you are living in the world fo complex numbers, then for example \(\sqrt{-9}=3\sqrt{-1}\) or \(3i\)