evaluate sqrt(-3)*sqrt(-12)
In many modern treatments, we agree that $\displaystyle \sqrt{-3}$ in not defined.
However we can enlarge the number system by one symbol. We say that $\displaystyle i$ is a solution for $\displaystyle x^2+1=0$.
In effect we now have $\displaystyle i^2=-1$. Now we can say $\displaystyle \sqrt{-3}=\sqrt{3}\;i$.
So now your question becomes $\displaystyle (\sqrt{3}\;i)(\sqrt{12}\;i)=-\sqrt{36}$