Answer
$13\sqrt[3]{2}$
Work Step by Step
Simplify each radicand to obtain
$5\sqrt[3]{8(2)}+\sqrt[3]{27(2)}
\\=5\sqrt[3]{2^3(2)}+\sqrt[3]{3^3(2)}
\\=5\cdot2\sqrt[3]{2} + 3\sqrt [3]{2}
\\=10\sqrt[3]{2} + 3\sqrt[3]{2}.$
RECALL:
The distributive property states that for any real numbers a, b, and c,
$ac + bc = (a+b)c.$
Use the distributive to obtain
$(10+3)\sqrt[3]{2}
\\=13\sqrt[3]{2}.$
