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

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

\(\sqrt{20} = \sqrt{4} ⋅ \sqrt{5} = 2 \sqrt{5} \text{.}\)

\(-4 \sqrt{80} = -4 ⋅ \sqrt{16} ⋅ \sqrt{5} = -4 ⋅ 4 ⋅ \sqrt{5} = -16 \sqrt{5} \text{.}\)

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

\(3 ⋅ 3 ⋅ \sqrt{2} - 4 ⋅ 2 ⋅ \sqrt{2} = 9 \sqrt{2} - 8 \sqrt{2} = 1 \sqrt{2} \text{.}\)

\(\sqrt{2\frac{7}{9}} = \sqrt{\frac{25}{9}} = {\sqrt{25} \over \sqrt{9}} = \frac{5}{3} = 1\frac{2}{3} \text{.}\)

\({7 \over 5 \sqrt{7}} = {7 \over 5 \sqrt{7}} ⋅ {\sqrt{7} \over \sqrt{7}} = {7 \sqrt{7} \over 5 ⋅ 7} = \frac{1}{5} \sqrt{7} \text{.}\)

\(\sqrt{2\frac{8}{9}} = \sqrt{\frac{26}{9}} = {\sqrt{26} \over \sqrt{9}} = {\sqrt{26} \over 3} = \frac{1}{3} \sqrt{26} \text{.}\)

\(\sqrt{\frac{25}{28}} = {\sqrt{25} \over \sqrt{28}} = {5 \over \sqrt{28}} ⋅ {\sqrt{28} \over \sqrt{28}} = {5 \sqrt{28} \over 28} = \frac{5}{28} \sqrt{28} = \frac{5}{28} ⋅ 2 ⋅ \sqrt{7} = \frac{5}{14} \sqrt{7} \text{.}\)

\(\sqrt{\frac{5}{11}} = {\sqrt{5} \over \sqrt{11}} ⋅ {\sqrt{11} \over \sqrt{11}} = {\sqrt{55} \over 11} = \frac{1}{11} \sqrt{55} \text{.}\)

\({48 \sqrt{40} \over 8 \sqrt{2}} = {48 \over 8} ⋅ {\sqrt{40} \over \sqrt{2}} = 6 \sqrt{20} = 6 ⋅ \sqrt{4} ⋅ \sqrt{5} = 6 ⋅ 2 ⋅ \sqrt{5} = 12 \sqrt{5}\)

\(3 \sqrt{2} ⋅ 5 \sqrt{6} = 15 \sqrt{12} = 15 ⋅ \sqrt{4} ⋅ \sqrt{3} = 15 ⋅ 2 ⋅ \sqrt{3} = 30 \sqrt{3}\)