Answer
$6\sqrt{5}-11x\sqrt[3]{5}$
Work Step by Step
Using properties of radicals, the expression $
3\sqrt{20}-7x\sqrt[3]{40}+3\sqrt[3]{5x^3}
$ simplifies to
\begin{array}{l}
3\sqrt{4\cdot5}-7x\sqrt[3]{8\cdot5}+3\sqrt[3]{x^3\cdot5}
\\=
3\cdot2\sqrt{5}-7x\cdot2\sqrt[3]{5}+3\cdot x\sqrt[3]{5}
\\=
6\sqrt{5}-14x\sqrt[3]{5}+3x\sqrt[3]{5}
\\=
6\sqrt{5}-11x\sqrt[3]{5}
.\end{array}