Answer
$13\sqrt[3]{2}$
Work Step by Step
Simplify each radical to obtain:
$=5\sqrt[3]{8(2)} + \sqrt[3]{27(2)}
\\=5\sqrt[3]{2^3(2)} + \sqrt[3]{3^3(2)}
\\=5(2)\sqrt[3]{2} + 3\sqrt[3]{2}
\\=10\sqrt[3]{2} + 3\sqrt[3]{2}$
RECALL:
The distributive property states that for any real numbers a, b, and c:
(1) $ac + bc = (a+b)c$
(2) $ac-bc=(a-b)c$
Use rule (1) above to combine like terms and obtain:
$=(10+3)\sqrt[3]{2}
\\=13\sqrt[3]{2}$
