Answer
$\sqrt{-75}-\sqrt{-12}=0+3\sqrt{3}i$
Work Step by Step
$\sqrt{-75}-\sqrt{-12}$
Substitute $\sqrt{-75}$ by $(\sqrt{-1})(\sqrt{75})$ and $\sqrt{-12}$ by $(\sqrt{-1})(\sqrt{12})$:
$\sqrt{-75}-\sqrt{-12}=(\sqrt{-1})(\sqrt{75})-(\sqrt{-1})(\sqrt{12})=...$
Substitute $\sqrt{-1}$ by $i$:
$...=\sqrt{75}i-\sqrt{12}i$:
Simplify:
$...=5\sqrt{3}i-2\sqrt{3}i=(5\sqrt{3}-2\sqrt{3})i=3\sqrt{3}i$
