College Algebra (11th Edition)

$7\sqrt[3]{3}$
$\bf{\text{Solution Outline:}}$ To add/subtract the given expression, $2\sqrt[3]{3}+4\sqrt[3]{24}-\sqrt[3]{81} ,$ simplify first each radical term by extracting the factor that is a perfect power of the index. Then, combine the like radicals. $\bf{\text{Solution Details:}}$ Extracting the factors of each radicand that is a perfect power of the index results to \begin{array}{l}\require{cancel} 2\sqrt[3]{3}+4\sqrt[3]{8\cdot3}-\sqrt[3]{27\cdot3} \\\\= 2\sqrt[3]{3}+4\sqrt[3]{(2)^3\cdot3}-\sqrt[3]{(3)^3\cdot3} \\\\= 2\sqrt[3]{3}+4(2)\sqrt[3]{3}-3\sqrt[3]{3} \\\\= 2\sqrt[3]{3}+8\sqrt[3]{3}-3\sqrt[3]{3} .\end{array} By combining the like radicals, the expression above simplifies to \begin{array}{l}\require{cancel} (2+8-3)\sqrt[3]{3} \\\\= 7\sqrt[3]{3} .\end{array}