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

\(6 \sqrt{75} = 6 ⋅ \sqrt{25} ⋅ \sqrt{3} = 6 ⋅ 5 ⋅ \sqrt{3} = 30 \sqrt{3} \text{.}\)

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

\({28 \sqrt{100} \over 7 \sqrt{5}} = {28 \over 7} ⋅ {\sqrt{100} \over \sqrt{5}} = 4 \sqrt{20} = 4 ⋅ \sqrt{4} ⋅ \sqrt{5} = 4 ⋅ 2 ⋅ \sqrt{5} = 8 \sqrt{5}\)

\(\sqrt{1\frac{11}{36}} = \sqrt{\frac{47}{36}} = {\sqrt{47} \over \sqrt{36}} = {\sqrt{47} \over 6} = \frac{1}{6} \sqrt{47} \text{.}\)

\(\sqrt{8} + \sqrt{18} = \sqrt{4} ⋅ \sqrt{2} + \sqrt{9} ⋅ \sqrt{2} = 2 \sqrt{2} + 3 \sqrt{2} \text{.}\)

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

\(2 \sqrt{12} + 7 \sqrt{300} = 2 ⋅ \sqrt{4} ⋅ \sqrt{3} + 7 ⋅ \sqrt{100} ⋅ \sqrt{3} \text{.}\)

\(2 ⋅ 2 ⋅ \sqrt{3} + 7 ⋅ 10 ⋅ \sqrt{3} = 4 \sqrt{3} + 70 \sqrt{3} = 74 \sqrt{3} \text{.}\)

\({4 \over 3 \sqrt{7}} = {4 \over 3 \sqrt{7}} ⋅ {\sqrt{7} \over \sqrt{7}} = {4 \sqrt{7} \over 3 ⋅ 7} = \frac{4}{21} \sqrt{7} \text{.}\)

\(\sqrt{1\frac{5}{76}} = \sqrt{\frac{81}{76}} = {\sqrt{81} \over \sqrt{76}} = {9 \over \sqrt{76}} ⋅ {\sqrt{76} \over \sqrt{76}} = {9 \sqrt{76} \over 76} = \frac{9}{76} \sqrt{76} = \frac{9}{76} ⋅ 2 ⋅ \sqrt{19} = \frac{9}{38} \sqrt{19} \text{.}\)

\(\sqrt{\frac{5}{8}} = {\sqrt{5} \over \sqrt{8}} ⋅ {\sqrt{8} \over \sqrt{8}} = {\sqrt{40} \over 8} = \frac{1}{8} \sqrt{40} = \frac{1}{8} ⋅ 2 ⋅ \sqrt{10} = \frac{1}{4} \sqrt{10} \text{.}\)