Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 24

$2i+2i\sqrt{3}$

Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $ \sqrt{-4}+\sqrt{-12} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{4}\cdot\sqrt{-1}+\sqrt{12}\cdot\sqrt{-1} \\\\= \sqrt{4}\cdot i+\sqrt{4\cdot3}\cdot i \\\\= \sqrt{(2)^2}\cdot i+\sqrt{(2)^2\cdot3}\cdot i \\\\= 2i+2i\sqrt{3} .\end{array}