Answer
$4i$
Work Step by Step
Use the definition of the square roots of negative numbers:
$\sqrt {-16} = \sqrt {(-1)(16)}$
Use the multiplication property of square roots to rewrite the radical:
$\sqrt {(-1)(16)} = \sqrt {-1} \cdot \sqrt {16}$
Use the definition of $i$ to substitute for $\sqrt {-1}$:
$i \cdot \sqrt {16}$
Take the square root of $16$:
$4i$
