Answer
$20y\sqrt[]{2y}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
5y\sqrt[]{8y}+2\sqrt[]{50y^3}
\\=
5y\sqrt[]{4\cdot2y}+2\sqrt[]{25y^2\cdot2y}
\\=
5y\cdot2\sqrt[]{2y}+2\cdot5y\sqrt[]{2y}
\\=
10y\sqrt[]{2y}+10y\sqrt[]{2y}
\\=
20y\sqrt[]{2y}
.\end{array}