Answer
$17\sqrt[4]{3x^3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
5\sqrt[4]{243x^3}+2\sqrt[4]{3x^3}
,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals.
$\bf{\text{Solution Details:}}$
Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
5\sqrt[4]{81\cdot3x^3}+2\sqrt[4]{3x^3}
\\\\=
5\sqrt[4]{(3)^4\cdot3x^3}+2\sqrt[4]{3x^3}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
5(3)\sqrt[4]{3x^3}+2\sqrt[4]{3x^3}
\\\\=
15\sqrt[4]{3x^3}+2\sqrt[4]{3x^3}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(15+2)\sqrt[4]{3x^3}
\\\\=
17\sqrt[4]{3x^3}
.\end{array}
