Answer
$6 \sqrt[3] {2}$
Work Step by Step
Factor the radicand so that we can take the cube roots later:
$\sqrt[3]{125(2)} + \sqrt[3] {27(2)} - \sqrt[3] {8(2)}$
$=\sqrt[3] {5^3 \cdot 2} + \sqrt[3] {3^3 \cdot 2} - \sqrt[3] {2^3 \cdot 2}$
Take the cube roots:
$=5\sqrt[3] {2} + 3 \sqrt[3] {2} - 2 \sqrt[3] {2}$
Since all terms have the same radical, add or subtract the coefficients from left to right, keeping the radical as-is:
$=(5+3-2)\sqrt[3]{2}\\
=6 \sqrt[3] {2}$
