\(\sqrt{80} = \sqrt{16} ⋅ \sqrt{5} = 4 \sqrt{5} \text{.}\)

\(7 \sqrt{45} = 7 ⋅ \sqrt{9} ⋅ \sqrt{5} = 7 ⋅ 3 ⋅ \sqrt{5} = 21 \sqrt{5} \text{.}\)

\(\sqrt{3\frac{6}{25}} = \sqrt{\frac{81}{25}} = {\sqrt{81} \over \sqrt{25}} = \frac{9}{5} = 1\frac{4}{5} \text{.}\)

\({14 \sqrt{196} \over 7 \sqrt{7}} = {14 \over 7} ⋅ {\sqrt{196} \over \sqrt{7}} = 2 \sqrt{28} = 2 ⋅ \sqrt{4} ⋅ \sqrt{7} = 2 ⋅ 2 ⋅ \sqrt{7} = 4 \sqrt{7}\)

\(\sqrt{8\frac{2}{9}} = \sqrt{\frac{74}{9}} = {\sqrt{74} \over \sqrt{9}} = {\sqrt{74} \over 3} = \frac{1}{3} \sqrt{74} \text{.}\)

\(\sqrt{125} + \sqrt{20} = \sqrt{25} ⋅ \sqrt{5} + \sqrt{4} ⋅ \sqrt{5} = 5 \sqrt{5} + 2 \sqrt{5} \text{.}\)

\(5 \sqrt{5} + 2 \sqrt{5} = 7 \sqrt{5} \text{.}\)

\(2 \sqrt{50} - 7 \sqrt{8} = 2 ⋅ \sqrt{25} ⋅ \sqrt{2} - 7 ⋅ \sqrt{4} ⋅ \sqrt{2} \text{.}\)

\(2 ⋅ 5 ⋅ \sqrt{2} - 7 ⋅ 2 ⋅ \sqrt{2} = 10 \sqrt{2} - 14 \sqrt{2} = -4 \sqrt{2} \text{.}\)

\({5 \over 7 \sqrt{3}} = {5 \over 7 \sqrt{3}} ⋅ {\sqrt{3} \over \sqrt{3}} = {5 \sqrt{3} \over 7 ⋅ 3} = \frac{5}{21} \sqrt{3} \text{.}\)

\(\sqrt{1\frac{29}{52}} = \sqrt{\frac{81}{52}} = {\sqrt{81} \over \sqrt{52}} = {9 \over \sqrt{52}} ⋅ {\sqrt{52} \over \sqrt{52}} = {9 \sqrt{52} \over 52} = \frac{9}{52} \sqrt{52} = \frac{9}{52} ⋅ 2 ⋅ \sqrt{13} = \frac{9}{26} \sqrt{13} \text{.}\)

\(\sqrt{\frac{2}{45}} = {\sqrt{2} \over \sqrt{45}} ⋅ {\sqrt{45} \over \sqrt{45}} = {\sqrt{90} \over 45} = \frac{1}{45} \sqrt{90} = \frac{1}{45} ⋅ 3 ⋅ \sqrt{10} = \frac{1}{15} \sqrt{10} \text{.}\)