\(\sqrt{48} + \sqrt{27} = \sqrt{16} ⋅ \sqrt{3} + \sqrt{9} ⋅ \sqrt{3} = 4 \sqrt{3} + 3 \sqrt{3} \text{.}\)

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

\(\sqrt{300} = \sqrt{100} ⋅ \sqrt{3} = 10 \sqrt{3} \text{.}\)

\(-6 \sqrt{20} = -6 ⋅ \sqrt{4} ⋅ \sqrt{5} = -6 ⋅ 2 ⋅ \sqrt{5} = -12 \sqrt{5} \text{.}\)

\(2 \sqrt{75} + 5 \sqrt{48} = 2 ⋅ \sqrt{25} ⋅ \sqrt{3} + 5 ⋅ \sqrt{16} ⋅ \sqrt{3} \text{.}\)

\(2 ⋅ 5 ⋅ \sqrt{3} + 5 ⋅ 4 ⋅ \sqrt{3} = 10 \sqrt{3} + 20 \sqrt{3} = 30 \sqrt{3} \text{.}\)

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

\({8 \over 3 \sqrt{7}} = {8 \over 3 \sqrt{7}} ⋅ {\sqrt{7} \over \sqrt{7}} = {8 \sqrt{7} \over 3 ⋅ 7} = \frac{8}{21} \sqrt{7} \text{.}\)

\(\sqrt{\frac{11}{16}} = {\sqrt{11} \over \sqrt{16}} = {\sqrt{11} \over 4} = \frac{1}{4} \sqrt{11} \text{.}\)

\(\sqrt{\frac{4}{53}} = {\sqrt{4} \over \sqrt{53}} = {2 \over \sqrt{53}} ⋅ {\sqrt{53} \over \sqrt{53}} = {2 \sqrt{53} \over 53} = \frac{2}{53} \sqrt{53} \text{.}\)

\(\sqrt{22\frac{1}{2}} = \sqrt{\frac{45}{2}} = {\sqrt{45} \over \sqrt{2}} ⋅ {\sqrt{2} \over \sqrt{2}} = {\sqrt{90} \over 2} = \frac{1}{2} \sqrt{90} = \frac{1}{2} ⋅ 3 ⋅ \sqrt{10} = 1\frac{1}{2} \sqrt{10} \text{.}\)

\({72 \sqrt{80} \over 9 \sqrt{10}} = {72 \over 9} ⋅ {\sqrt{80} \over \sqrt{10}} = 8 \sqrt{8} = 8 ⋅ \sqrt{4} ⋅ \sqrt{2} = 8 ⋅ 2 ⋅ \sqrt{2} = 16 \sqrt{2}\)

\(4 \sqrt{14} ⋅ 3 \sqrt{2} = 12 \sqrt{28} = 12 ⋅ \sqrt{4} ⋅ \sqrt{7} = 12 ⋅ 2 ⋅ \sqrt{7} = 24 \sqrt{7}\)