Answer
$\sqrt{-9}+\sqrt{-16}=3i+4i=7i$.
Work Step by Step
The given expression is
$=\sqrt{-9}+\sqrt{-16}$
Rewrite as shown below.
$=\sqrt{9}\cdot \sqrt {-1}+\sqrt{16}\cdot \sqrt {-1}$
$=\sqrt{3^2}\cdot \sqrt {-1}+\sqrt{4^2}\cdot \sqrt {-1}$
Use $ \sqrt {-1}=i$
$=3i+4i$
Add both terms.
$=7i$.
