\(\sqrt{32} + \sqrt{8} = \sqrt{16} ⋅ \sqrt{2} + \sqrt{4} ⋅ \sqrt{2} = 4 \sqrt{2} + 2 \sqrt{2} \text{.}\)

\(4 \sqrt{2} + 2 \sqrt{2} = 6 \sqrt{2} \text{.}\)

\(\sqrt{112} = \sqrt{16} ⋅ \sqrt{7} = 4 \sqrt{7} \text{.}\)

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

\(7 \sqrt{20} - 5 \sqrt{45} = 7 ⋅ \sqrt{4} ⋅ \sqrt{5} - 5 ⋅ \sqrt{9} ⋅ \sqrt{5} \text{.}\)

\(7 ⋅ 2 ⋅ \sqrt{5} - 5 ⋅ 3 ⋅ \sqrt{5} = 14 \sqrt{5} - 15 \sqrt{5} = -1 \sqrt{5} \text{.}\)

\(\sqrt{2\frac{2}{49}} = \sqrt{\frac{100}{49}} = {\sqrt{100} \over \sqrt{49}} = \frac{10}{7} = 1\frac{3}{7} \text{.}\)

\({8 \over 7 \sqrt{5}} = {8 \over 7 \sqrt{5}} ⋅ {\sqrt{5} \over \sqrt{5}} = {8 \sqrt{5} \over 7 ⋅ 5} = \frac{8}{35} \sqrt{5} \text{.}\)

\(\sqrt{2\frac{25}{36}} = \sqrt{\frac{97}{36}} = {\sqrt{97} \over \sqrt{36}} = {\sqrt{97} \over 6} = \frac{1}{6} \sqrt{97} \text{.}\)

\(\sqrt{1\frac{23}{58}} = \sqrt{\frac{81}{58}} = {\sqrt{81} \over \sqrt{58}} = {9 \over \sqrt{58}} ⋅ {\sqrt{58} \over \sqrt{58}} = {9 \sqrt{58} \over 58} = \frac{9}{58} \sqrt{58} \text{.}\)

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

\({8 \sqrt{60} \over \sqrt{3}} = 8 ⋅ {\sqrt{60} \over \sqrt{3}} = 8 \sqrt{20} = 8 ⋅ \sqrt{4} ⋅ \sqrt{5} = 8 ⋅ 2 ⋅ \sqrt{5} = 16 \sqrt{5}\)

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