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

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

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

\(-5 \sqrt{8} = -5 ⋅ \sqrt{4} ⋅ \sqrt{2} = -5 ⋅ 2 ⋅ \sqrt{2} = -10 \sqrt{2} \text{.}\)

\(5 \sqrt{27} - 2 \sqrt{300} = 5 ⋅ \sqrt{9} ⋅ \sqrt{3} - 2 ⋅ \sqrt{100} ⋅ \sqrt{3} \text{.}\)

\(5 ⋅ 3 ⋅ \sqrt{3} - 2 ⋅ 10 ⋅ \sqrt{3} = 15 \sqrt{3} - 20 \sqrt{3} = -5 \sqrt{3} \text{.}\)

\(\sqrt{\frac{16}{49}} = {\sqrt{16} \over \sqrt{49}} = \frac{4}{7} \text{.}\)

\({7 \over 3 \sqrt{5}} = {7 \over 3 \sqrt{5}} ⋅ {\sqrt{5} \over \sqrt{5}} = {7 \sqrt{5} \over 3 ⋅ 5} = \frac{7}{15} \sqrt{5} \text{.}\)

\(\sqrt{1\frac{21}{25}} = \sqrt{\frac{46}{25}} = {\sqrt{46} \over \sqrt{25}} = {\sqrt{46} \over 5} = \frac{1}{5} \sqrt{46} \text{.}\)

\(\sqrt{\frac{1}{18}} = {\sqrt{1} \over \sqrt{18}} = {1 \over \sqrt{18}} ⋅ {\sqrt{18} \over \sqrt{18}} = {\sqrt{18} \over 18} = \frac{1}{18} \sqrt{18} = \frac{1}{18} ⋅ 3 ⋅ \sqrt{2} = \frac{1}{6} \sqrt{2} \text{.}\)

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

\({42 \sqrt{48} \over 7 \sqrt{2}} = {42 \over 7} ⋅ {\sqrt{48} \over \sqrt{2}} = 6 \sqrt{24} = 6 ⋅ \sqrt{4} ⋅ \sqrt{6} = 6 ⋅ 2 ⋅ \sqrt{6} = 12 \sqrt{6}\)

\(5 \sqrt{2} ⋅ 4 \sqrt{6} = 20 \sqrt{12} = 20 ⋅ \sqrt{4} ⋅ \sqrt{3} = 20 ⋅ 2 ⋅ \sqrt{3} = 40 \sqrt{3}\)