$\sqrt{98}-\sqrt{50}+\sqrt{32}=\sqrt{49\ast 2}-\sqrt{25\ast 2}+\sqrt{16\ast 2}=7\sqrt{2}-5\sqrt{2}+4\sqrt{2}=6\sqrt{2}$

$3\sqrt{8}+\sqrt{128}-\frac{1}{3}\sqrt{162}=3\sqrt{4\ast 2}+\sqrt{64\ast 2}-\frac{1}{3}\sqrt{81\ast 2}=3\ast 2\sqrt{2}+8\sqrt{2}-\frac{1}{3}\ast 9\sqrt{2}=6\sqrt{2}+8\sqrt{2}-3\sqrt{2}=11\sqrt{2}$

$0,7\sqrt{300}-7\sqrt{\frac{3}{49}}+\frac{2}{3}\sqrt{108}=0,7\sqrt{100\ast 3}-7\sqrt{\frac{1}{49}\ast 3}+\frac{2}{3}\sqrt{36\ast 3}=0,7\ast 10\sqrt{3}-7\ast \frac{1}{7}\sqrt{3}+\frac{2}{3}\ast 6\sqrt{3}=7\sqrt{3}-\sqrt{3}+2\ast 2\sqrt{3}=6\sqrt{3}+4\sqrt{3}=10\sqrt{3}$

$\sqrt{5a}-2\sqrt{20a}+3\sqrt{80a}=\sqrt{5a}-2\sqrt{4\ast 5a}+3\sqrt{16\ast 5a}=\sqrt{5a}-2\ast 2\sqrt{5a}+3\ast 4\sqrt{5a}=\sqrt{5a}-4\sqrt{5a}+12\sqrt{5a}=9\sqrt{5a}$

$\sqrt{a^{3}b}-\frac{2}{a}\sqrt{a^{5}b}=\sqrt{a^2\ast ab}-\frac{2}{a}\sqrt{a^4\ast ab}=a\sqrt{ab}-\frac{2}{a}\ast a^2\sqrt{ab}=a\sqrt{ab}-2a\sqrt{ab}=-a\sqrt{ab}$, если a > 0

$\sqrt{c^5}+4c\sqrt{c^3}-5c^2\sqrt{c}=\sqrt{c^4\ast c}+4c\sqrt{c^2\ast c}-5c^2\sqrt{c}=c^2\sqrt{c}+4c\ast c\sqrt{c}-5c^2\sqrt{c}=c^2\sqrt{c}+4c^2\sqrt{c}-5c^2\sqrt{c}=0$