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

\(-7 \sqrt{500} = -7 ⋅ \sqrt{100} ⋅ \sqrt{5} = -7 ⋅ 10 ⋅ \sqrt{5} = -70 \sqrt{5} \text{.}\)

\(\sqrt{\frac{1}{64}} = {\sqrt{1} \over \sqrt{64}} = \frac{1}{8} \text{.}\)

\({18 \sqrt{36} \over 9 \sqrt{3}} = {18 \over 9} ⋅ {\sqrt{36} \over \sqrt{3}} = 2 \sqrt{12} = 2 ⋅ \sqrt{4} ⋅ \sqrt{3} = 2 ⋅ 2 ⋅ \sqrt{3} = 4 \sqrt{3}\)

\(\sqrt{\frac{8}{81}} = {\sqrt{8} \over \sqrt{81}} = {\sqrt{8} \over 9} = \frac{1}{9} \sqrt{8} = \frac{1}{9} ⋅ 2 ⋅ \sqrt{2} = \frac{2}{9} \sqrt{2} \text{.}\)