Answer
$\sqrt[6]{5,400}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[3]{5}\cdot\sqrt{6}
,$ express the radicals as radicals with same indices by finding the $LCD$ of the indices. Once the indices are the same, use the laws of radicals to simplify the expression.
$\bf{\text{Solution Details:}}$
The $LCD$ of the indices, $
3
$ and $
2
,$ is $
6
$ since it is the lowest number that can be divided exactly by both indices. Multiplying the index by a number to make it equal to the $LCD$ and raising the radicand by the same multiplier results to
\begin{array}{l}\require{cancel}
\sqrt[3(2)]{5^2}\cdot\sqrt[2(3)]{6^3}
\\\\=
\sqrt[6]{25}\cdot\sqrt[6]{216}
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\sqrt[6]{25(216)}
\\\\=
\sqrt[6]{5,400}
.\end{array}
