\(\sqrt{200} + \sqrt{50} = \sqrt{100} ⋅ \sqrt{2} + \sqrt{25} ⋅ \sqrt{2} = 10 \sqrt{2} + 5 \sqrt{2} \text{.}\)

\(10 \sqrt{2} + 5 \sqrt{2} = 15 \sqrt{2} \text{.}\)

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

\(-7 \sqrt{18} = -7 ⋅ \sqrt{9} ⋅ \sqrt{2} = -7 ⋅ 3 ⋅ \sqrt{2} = -21 \sqrt{2} \text{.}\)

\(5 \sqrt{200} + 4 \sqrt{18} = 5 ⋅ \sqrt{100} ⋅ \sqrt{2} + 4 ⋅ \sqrt{9} ⋅ \sqrt{2} \text{.}\)

\(5 ⋅ 10 ⋅ \sqrt{2} + 4 ⋅ 3 ⋅ \sqrt{2} = 50 \sqrt{2} + 12 \sqrt{2} = 62 \sqrt{2} \text{.}\)

\(\sqrt{3\frac{6}{25}} = \sqrt{\frac{81}{25}} = {\sqrt{81} \over \sqrt{25}} = \frac{9}{5} = 1\frac{4}{5} \text{.}\)