Answer
$7\sqrt[3]{3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
