\(\sqrt{48} + \sqrt{75} = \sqrt{16} ⋅ \sqrt{3} + \sqrt{25} ⋅ \sqrt{3} = 4 \sqrt{3} + 5 \sqrt{3} \text{.}\)

\(4 \sqrt{3} + 5 \sqrt{3} = 9 \sqrt{3} \text{.}\)

\(\sqrt{50} = \sqrt{25} ⋅ \sqrt{2} = 5 \sqrt{2} \text{.}\)

\(6 \sqrt{48} = 6 ⋅ \sqrt{16} ⋅ \sqrt{3} = 6 ⋅ 4 ⋅ \sqrt{3} = 24 \sqrt{3} \text{.}\)

\(7 \sqrt{50} - 4 \sqrt{200} = 7 ⋅ \sqrt{25} ⋅ \sqrt{2} - 4 ⋅ \sqrt{100} ⋅ \sqrt{2} \text{.}\)

\(7 ⋅ 5 ⋅ \sqrt{2} - 4 ⋅ 10 ⋅ \sqrt{2} = 35 \sqrt{2} - 40 \sqrt{2} = -5 \sqrt{2} \text{.}\)

\(\sqrt{1\frac{11}{25}} = \sqrt{\frac{36}{25}} = {\sqrt{36} \over \sqrt{25}} = \frac{6}{5} = 1\frac{1}{5} \text{.}\)

\({7 \over 3 \sqrt{7}} = {7 \over 3 \sqrt{7}} ⋅ {\sqrt{7} \over \sqrt{7}} = {7 \sqrt{7} \over 3 ⋅ 7} = \frac{1}{3} \sqrt{7} \text{.}\)

\(\sqrt{\frac{11}{64}} = {\sqrt{11} \over \sqrt{64}} = {\sqrt{11} \over 8} = \frac{1}{8} \sqrt{11} \text{.}\)

\(\sqrt{\frac{1}{12}} = {\sqrt{1} \over \sqrt{12}} = {1 \over \sqrt{12}} ⋅ {\sqrt{12} \over \sqrt{12}} = {\sqrt{12} \over 12} = \frac{1}{12} \sqrt{12} = \frac{1}{12} ⋅ 2 ⋅ \sqrt{3} = \frac{1}{6} \sqrt{3} \text{.}\)

\(\sqrt{10\frac{1}{3}} = \sqrt{\frac{31}{3}} = {\sqrt{31} \over \sqrt{3}} ⋅ {\sqrt{3} \over \sqrt{3}} = {\sqrt{93} \over 3} = \frac{1}{3} \sqrt{93} \text{.}\)

\({36 \sqrt{60} \over 4 \sqrt{3}} = {36 \over 4} ⋅ {\sqrt{60} \over \sqrt{3}} = 9 \sqrt{20} = 9 ⋅ \sqrt{4} ⋅ \sqrt{5} = 9 ⋅ 2 ⋅ \sqrt{5} = 18 \sqrt{5}\)

\(3 \sqrt{7} ⋅ 5 \sqrt{14} = 15 \sqrt{98} = 15 ⋅ \sqrt{49} ⋅ \sqrt{2} = 15 ⋅ 7 ⋅ \sqrt{2} = 105 \sqrt{2}\)