\(\sqrt{50} = \sqrt{25} ⋅ \sqrt{2} = 5 \sqrt{2} \text{.}\)

\(-2 \sqrt{200} = -2 ⋅ \sqrt{100} ⋅ \sqrt{2} = -2 ⋅ 10 ⋅ \sqrt{2} = -20 \sqrt{2} \text{.}\)

\(\sqrt{\frac{16}{25}} = {\sqrt{16} \over \sqrt{25}} = \frac{4}{5} \text{.}\)

\({30 \sqrt{240} \over 6 \sqrt{6}} = {30 \over 6} ⋅ {\sqrt{240} \over \sqrt{6}} = 5 \sqrt{40} = 5 ⋅ \sqrt{4} ⋅ \sqrt{10} = 5 ⋅ 2 ⋅ \sqrt{10} = 10 \sqrt{10}\)

\(\sqrt{1\frac{5}{9}} = \sqrt{\frac{14}{9}} = {\sqrt{14} \over \sqrt{9}} = {\sqrt{14} \over 3} = \frac{1}{3} \sqrt{14} \text{.}\)