\(\sqrt{48} = \sqrt{16} ⋅ \sqrt{3} = 4 \sqrt{3} \text{.}\)

\(6 \sqrt{45} = 6 ⋅ \sqrt{9} ⋅ \sqrt{5} = 6 ⋅ 3 ⋅ \sqrt{5} = 18 \sqrt{5} \text{.}\)

\(\sqrt{\frac{49}{81}} = {\sqrt{49} \over \sqrt{81}} = \frac{7}{9} \text{.}\)

\({14 \sqrt{72} \over 7 \sqrt{3}} = {14 \over 7} ⋅ {\sqrt{72} \over \sqrt{3}} = 2 \sqrt{24} = 2 ⋅ \sqrt{4} ⋅ \sqrt{6} = 2 ⋅ 2 ⋅ \sqrt{6} = 4 \sqrt{6}\)

\(\sqrt{2\frac{2}{25}} = \sqrt{\frac{52}{25}} = {\sqrt{52} \over \sqrt{25}} = {\sqrt{52} \over 5} = \frac{1}{5} \sqrt{52} = \frac{1}{5} ⋅ 2 ⋅ \sqrt{13} = \frac{2}{5} \sqrt{13} \text{.}\)

\(\sqrt{200} + \sqrt{18} = \sqrt{100} ⋅ \sqrt{2} + \sqrt{9} ⋅ \sqrt{2} = 10 \sqrt{2} + 3 \sqrt{2} \text{.}\)

\(10 \sqrt{2} + 3 \sqrt{2} = 13 \sqrt{2} \text{.}\)

\(5 \sqrt{300} + 3 \sqrt{12} = 5 ⋅ \sqrt{100} ⋅ \sqrt{3} + 3 ⋅ \sqrt{4} ⋅ \sqrt{3} \text{.}\)

\(5 ⋅ 10 ⋅ \sqrt{3} + 3 ⋅ 2 ⋅ \sqrt{3} = 50 \sqrt{3} + 6 \sqrt{3} = 56 \sqrt{3} \text{.}\)

\({2 \over 7 \sqrt{7}} = {2 \over 7 \sqrt{7}} ⋅ {\sqrt{7} \over \sqrt{7}} = {2 \sqrt{7} \over 7 ⋅ 7} = \frac{2}{49} \sqrt{7} \text{.}\)

\(\sqrt{\frac{64}{65}} = {\sqrt{64} \over \sqrt{65}} = {8 \over \sqrt{65}} ⋅ {\sqrt{65} \over \sqrt{65}} = {8 \sqrt{65} \over 65} = \frac{8}{65} \sqrt{65} \text{.}\)

\(\sqrt{3\frac{3}{5}} = \sqrt{\frac{18}{5}} = {\sqrt{18} \over \sqrt{5}} ⋅ {\sqrt{5} \over \sqrt{5}} = {\sqrt{90} \over 5} = \frac{1}{5} \sqrt{90} = \frac{1}{5} ⋅ 3 ⋅ \sqrt{10} = \frac{3}{5} \sqrt{10} \text{.}\)