Answer
$19i\sqrt{2}$
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:
$=5\cdot i\sqrt{8}+3 \cdot i\sqrt{18}
\\=5i\sqrt{4(2)} + 3i\sqrt{9(2)}
\\=5i(\sqrt{2^2(2}) + 3i(\sqrt{3^2(2})$
Simplify each radical to obtain:
$=5i\cdot 2\sqrt{2} +3i \cdot 3 \sqrt{2}
\\=10i\sqrt{2} + 9i\sqrt{2}$
Combine like terms using the rule $ac+bc=(a+b)c$ to obtain:
$=(10i+9i)\sqrt{2}
\\=19i\sqrt{2}$
