Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set - Page 430: 41

$\sqrt[3]{6}+2$

Using the Distributive Property and the properties of radicals, the given expression, $ \sqrt[3]{2}(\sqrt[3]{3}+\sqrt[3]{4}) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{2}(\sqrt[3]{3})+\sqrt[3]{2}(\sqrt[3]{4}) \\\\= \sqrt[3]{6}+\sqrt[3]{8} \\\\= \sqrt[3]{6}+\sqrt[3]{(2)^3} \\\\= \sqrt[3]{6}+2 .\end{array}