Factor out perfect squares: $\displaystyle\sqrt{{{4}\cdot{4}\cdot{5}\cdot{{x}}^{{4}}\cdot{{y}}^{{2}}\cdot{y}}}\usepackage{cmbright}\Huge\$

Separate the factors into individual radicals: $\displaystyle\sqrt{{{{4}}^{{2}}}}\cdot\sqrt{{{5}}}\cdot\sqrt{{{{\left({{x}}^{{2}}\right)}}^{{2}}}}\cdot\sqrt{{{{y}}^{{2}}}}\cdot\sqrt{{{y}}}\usepackage{cmbright}\Huge\$

Find the square roots: $\displaystyle{4}\cdot{{x}}^{{2}}\cdot{\left|{y}\right|}\cdot\sqrt{{{5}{y}}}\usepackage{cmbright}\Huge\$

Simplify: $\displaystyle{4}{{x}}^{{2}}{\left|{y}\right|}\sqrt{{{5}{y}}}\usepackage{cmbright}\Huge\$