\(\sqrt{700} = \sqrt{100} ⋅ \sqrt{7} = 10 \sqrt{7} \text{.}\)

\(6 \sqrt{500} = 6 ⋅ \sqrt{100} ⋅ \sqrt{5} = 6 ⋅ 10 ⋅ \sqrt{5} = 60 \sqrt{5} \text{.}\)

\(\sqrt{\frac{25}{36}} = {\sqrt{25} \over \sqrt{36}} = \frac{5}{6} \text{.}\)

\({28 \sqrt{144} \over 4 \sqrt{6}} = {28 \over 4} ⋅ {\sqrt{144} \over \sqrt{6}} = 7 \sqrt{24} = 7 ⋅ \sqrt{4} ⋅ \sqrt{6} = 7 ⋅ 2 ⋅ \sqrt{6} = 14 \sqrt{6}\)

\(\sqrt{\frac{63}{64}} = {\sqrt{63} \over \sqrt{64}} = {\sqrt{63} \over 8} = \frac{1}{8} \sqrt{63} = \frac{1}{8} ⋅ 3 ⋅ \sqrt{7} = \frac{3}{8} \sqrt{7} \text{.}\)

\(\sqrt{500} + \sqrt{125} = \sqrt{100} ⋅ \sqrt{5} + \sqrt{25} ⋅ \sqrt{5} = 10 \sqrt{5} + 5 \sqrt{5} \text{.}\)

\(10 \sqrt{5} + 5 \sqrt{5} = 15 \sqrt{5} \text{.}\)

\(4 \sqrt{80} + 2 \sqrt{125} = 4 ⋅ \sqrt{16} ⋅ \sqrt{5} + 2 ⋅ \sqrt{25} ⋅ \sqrt{5} \text{.}\)

\(4 ⋅ 4 ⋅ \sqrt{5} + 2 ⋅ 5 ⋅ \sqrt{5} = 16 \sqrt{5} + 10 \sqrt{5} = 26 \sqrt{5} \text{.}\)

\({2 \over 3 \sqrt{2}} = {2 \over 3 \sqrt{2}} ⋅ {\sqrt{2} \over \sqrt{2}} = {2 \sqrt{2} \over 3 ⋅ 2} = \frac{1}{3} \sqrt{2} \text{.}\)

\(\sqrt{2\frac{2}{17}} = \sqrt{\frac{36}{17}} = {\sqrt{36} \over \sqrt{17}} = {6 \over \sqrt{17}} ⋅ {\sqrt{17} \over \sqrt{17}} = {6 \sqrt{17} \over 17} = \frac{6}{17} \sqrt{17} \text{.}\)

\(\sqrt{16\frac{2}{3}} = \sqrt{\frac{50}{3}} = {\sqrt{50} \over \sqrt{3}} ⋅ {\sqrt{3} \over \sqrt{3}} = {\sqrt{150} \over 3} = \frac{1}{3} \sqrt{150} = \frac{1}{3} ⋅ 5 ⋅ \sqrt{6} = 1\frac{2}{3} \sqrt{6} \text{.}\)