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

\(2 \sqrt{112} = 2 ⋅ \sqrt{16} ⋅ \sqrt{7} = 2 ⋅ 4 ⋅ \sqrt{7} = 8 \sqrt{7} \text{.}\)

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

\({56 \sqrt{160} \over 8 \sqrt{8}} = {56 \over 8} ⋅ {\sqrt{160} \over \sqrt{8}} = 7 \sqrt{20} = 7 ⋅ \sqrt{4} ⋅ \sqrt{5} = 7 ⋅ 2 ⋅ \sqrt{5} = 14 \sqrt{5}\)

\(\sqrt{4\frac{7}{16}} = \sqrt{\frac{71}{16}} = {\sqrt{71} \over \sqrt{16}} = {\sqrt{71} \over 4} = \frac{1}{4} \sqrt{71} \text{.}\)

\(\sqrt{18} + \sqrt{32} = \sqrt{9} ⋅ \sqrt{2} + \sqrt{16} ⋅ \sqrt{2} = 3 \sqrt{2} + 4 \sqrt{2} \text{.}\)

\(3 \sqrt{2} + 4 \sqrt{2} = 7 \sqrt{2} \text{.}\)

\(2 \sqrt{300} + 6 \sqrt{27} = 2 ⋅ \sqrt{100} ⋅ \sqrt{3} + 6 ⋅ \sqrt{9} ⋅ \sqrt{3} \text{.}\)

\(2 ⋅ 10 ⋅ \sqrt{3} + 6 ⋅ 3 ⋅ \sqrt{3} = 20 \sqrt{3} + 18 \sqrt{3} = 38 \sqrt{3} \text{.}\)

\({3 \over 5 \sqrt{7}} = {3 \over 5 \sqrt{7}} ⋅ {\sqrt{7} \over \sqrt{7}} = {3 \sqrt{7} \over 5 ⋅ 7} = \frac{3}{35} \sqrt{7} \text{.}\)

\(\sqrt{1\frac{22}{27}} = \sqrt{\frac{49}{27}} = {\sqrt{49} \over \sqrt{27}} = {7 \over \sqrt{27}} ⋅ {\sqrt{27} \over \sqrt{27}} = {7 \sqrt{27} \over 27} = \frac{7}{27} \sqrt{27} = \frac{7}{27} ⋅ 3 ⋅ \sqrt{3} = \frac{7}{9} \sqrt{3} \text{.}\)

\(\sqrt{\frac{2}{23}} = {\sqrt{2} \over \sqrt{23}} ⋅ {\sqrt{23} \over \sqrt{23}} = {\sqrt{46} \over 23} = \frac{1}{23} \sqrt{46} \text{.}\)

\(5 \sqrt{6} ⋅ 2 \sqrt{15} = 10 \sqrt{90} = 10 ⋅ \sqrt{9} ⋅ \sqrt{10} = 10 ⋅ 3 ⋅ \sqrt{10} = 30 \sqrt{10}\)