Answer
$47i$
Work Step by Step
RECALL:
(1) $\sqrt{-1}=i$
(2) For any real number $a\gt0$, $\sqrt{-a} = i\sqrt{a}$.
Use rule (2) above to obtain:
$=5\cdot i\sqrt{16}+3 \cdot i\sqrt{81}
\\=5i\sqrt{4^2} + 3i\sqrt{9^2}
\\=5i(4) + 3i(9)
\\=20i+27i
\\=(20+27)i
\\=47i$
