\(\sqrt{18} + \sqrt{50} = \sqrt{9} ⋅ \sqrt{2} + \sqrt{25} ⋅ \sqrt{2} = 3 \sqrt{2} + 5 \sqrt{2} \text{.}\)

\(3 \sqrt{2} + 5 \sqrt{2} = 8 \sqrt{2} \text{.}\)

\(\sqrt{175} = \sqrt{25} ⋅ \sqrt{7} = 5 \sqrt{7} \text{.}\)

\(3 \sqrt{28} = 3 ⋅ \sqrt{4} ⋅ \sqrt{7} = 3 ⋅ 2 ⋅ \sqrt{7} = 6 \sqrt{7} \text{.}\)

\(7 \sqrt{48} + 3 \sqrt{27} = 7 ⋅ \sqrt{16} ⋅ \sqrt{3} + 3 ⋅ \sqrt{9} ⋅ \sqrt{3} \text{.}\)

\(7 ⋅ 4 ⋅ \sqrt{3} + 3 ⋅ 3 ⋅ \sqrt{3} = 28 \sqrt{3} + 9 \sqrt{3} = 37 \sqrt{3} \text{.}\)

\(\sqrt{\frac{9}{25}} = {\sqrt{9} \over \sqrt{25}} = \frac{3}{5} \text{.}\)

\({5 \over 6 \sqrt{7}} = {5 \over 6 \sqrt{7}} ⋅ {\sqrt{7} \over \sqrt{7}} = {5 \sqrt{7} \over 6 ⋅ 7} = \frac{5}{42} \sqrt{7} \text{.}\)

\(\sqrt{\frac{26}{81}} = {\sqrt{26} \over \sqrt{81}} = {\sqrt{26} \over 9} = \frac{1}{9} \sqrt{26} \text{.}\)

\(\sqrt{2\frac{1}{12}} = \sqrt{\frac{25}{12}} = {\sqrt{25} \over \sqrt{12}} = {5 \over \sqrt{12}} ⋅ {\sqrt{12} \over \sqrt{12}} = {5 \sqrt{12} \over 12} = \frac{5}{12} \sqrt{12} = \frac{5}{12} ⋅ 2 ⋅ \sqrt{3} = \frac{5}{6} \sqrt{3} \text{.}\)

\(\sqrt{\frac{3}{8}} = {\sqrt{3} \over \sqrt{8}} ⋅ {\sqrt{8} \over \sqrt{8}} = {\sqrt{24} \over 8} = \frac{1}{8} \sqrt{24} = \frac{1}{8} ⋅ 2 ⋅ \sqrt{6} = \frac{1}{4} \sqrt{6} \text{.}\)

\({45 \sqrt{16} \over 5 \sqrt{2}} = {45 \over 5} ⋅ {\sqrt{16} \over \sqrt{2}} = 9 \sqrt{8} = 9 ⋅ \sqrt{4} ⋅ \sqrt{2} = 9 ⋅ 2 ⋅ \sqrt{2} = 18 \sqrt{2}\)

\(2 \sqrt{2} ⋅ 3 \sqrt{6} = 6 \sqrt{12} = 6 ⋅ \sqrt{4} ⋅ \sqrt{3} = 6 ⋅ 2 ⋅ \sqrt{3} = 12 \sqrt{3}\)