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

\(-7 \sqrt{125} = -7 ⋅ \sqrt{25} ⋅ \sqrt{5} = -7 ⋅ 5 ⋅ \sqrt{5} = -35 \sqrt{5} \text{.}\)

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

\({16 \sqrt{72} \over 8 \sqrt{3}} = {16 \over 8} ⋅ {\sqrt{72} \over \sqrt{3}} = 2 \sqrt{24} = 2 ⋅ \sqrt{4} ⋅ \sqrt{6} = 2 ⋅ 2 ⋅ \sqrt{6} = 4 \sqrt{6}\)

\(\sqrt{1\frac{11}{81}} = \sqrt{\frac{92}{81}} = {\sqrt{92} \over \sqrt{81}} = {\sqrt{92} \over 9} = \frac{1}{9} \sqrt{92} = \frac{1}{9} ⋅ 2 ⋅ \sqrt{23} = \frac{2}{9} \sqrt{23} \text{.}\)

\(\sqrt{12} + \sqrt{75} = \sqrt{4} ⋅ \sqrt{3} + \sqrt{25} ⋅ \sqrt{3} = 2 \sqrt{3} + 5 \sqrt{3} \text{.}\)

\(2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} \text{.}\)

\(4 \sqrt{500} - 6 \sqrt{45} = 4 ⋅ \sqrt{100} ⋅ \sqrt{5} - 6 ⋅ \sqrt{9} ⋅ \sqrt{5} \text{.}\)

\(4 ⋅ 10 ⋅ \sqrt{5} - 6 ⋅ 3 ⋅ \sqrt{5} = 40 \sqrt{5} - 18 \sqrt{5} = 22 \sqrt{5} \text{.}\)

\({4 \over 5 \sqrt{2}} = {4 \over 5 \sqrt{2}} ⋅ {\sqrt{2} \over \sqrt{2}} = {4 \sqrt{2} \over 5 ⋅ 2} = \frac{2}{5} \sqrt{2} \text{.}\)

\(\sqrt{\frac{25}{72}} = {\sqrt{25} \over \sqrt{72}} = {5 \over \sqrt{72}} ⋅ {\sqrt{72} \over \sqrt{72}} = {5 \sqrt{72} \over 72} = \frac{5}{72} \sqrt{72} = \frac{5}{72} ⋅ 6 ⋅ \sqrt{2} = \frac{5}{12} \sqrt{2} \text{.}\)

\(\sqrt{16\frac{1}{2}} = \sqrt{\frac{33}{2}} = {\sqrt{33} \over \sqrt{2}} ⋅ {\sqrt{2} \over \sqrt{2}} = {\sqrt{66} \over 2} = \frac{1}{2} \sqrt{66} \text{.}\)

\(2 \sqrt{6} ⋅ 5 \sqrt{2} = 10 \sqrt{12} = 10 ⋅ \sqrt{4} ⋅ \sqrt{3} = 10 ⋅ 2 ⋅ \sqrt{3} = 20 \sqrt{3}\)