Appendix G - Complex Numbers - G Exercises - Page A55: 14

$-6$

We use basic root properties to simplify ($\sqrt{a}\sqrt{b}=\sqrt{ab}$): $\sqrt{-3}\sqrt{-12}$ $\sqrt{3*-1}\sqrt{12*-1}$ $=\sqrt{3}i\sqrt{12}i$ $=\sqrt{3*12}i^{2}$ We use the fact that $i^2=-1$ (because $i=\sqrt{-1}$) $=\sqrt{36}*-1$ $=-6$