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

\(-6 \sqrt{20} = -6 ⋅ \sqrt{4} ⋅ \sqrt{5} = -6 ⋅ 2 ⋅ \sqrt{5} = -12 \sqrt{5} \text{.}\)

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

\({14 \sqrt{144} \over 2 \sqrt{6}} = {14 \over 2} ⋅ {\sqrt{144} \over \sqrt{6}} = 7 \sqrt{24} = 7 ⋅ \sqrt{4} ⋅ \sqrt{6} = 7 ⋅ 2 ⋅ \sqrt{6} = 14 \sqrt{6}\)