Решение:

1. $$0,2\sqrt{4900} = 0,2\cdot\sqrt{70^2} = 0,2\cdot 70 = 14$$
2. $$100\sqrt{0,04}-\frac{1}{17}\sqrt{289} = 100\cdot\sqrt{0,2^2}-\frac{1}{17}\cdot\sqrt{17^2} = 100\cdot 0,2 - \frac{1}{17}\cdot 17 = 20 - 1 = 19$$
3. $$\frac{7}{8}\cdot\sqrt{1\frac{15}{49}} = \frac{7}{8}\cdot\sqrt{\frac{64}{49}} = \frac{7}{8}\cdot\sqrt{\left(\frac{8}{7}\right)^2} = \frac{7}{8}\cdot\frac{8}{7} = 1$$
4. $$\sqrt{361}-10\sqrt{2,89} = \sqrt{19^2} - 10\cdot\sqrt{1,7^2} = 19 - 10\cdot 1,7 = 19 - 17 = 2$$
5. $$3,6\cdot\sqrt{0,25}+\frac{1}{32}\cdot\sqrt{256} = 3,6\cdot\sqrt{0,5^2} + \frac{1}{32}\cdot\sqrt{16^2} = 3,6\cdot 0,5 + \frac{1}{32}\cdot 16 = 1,8 + \frac{1}{2} = 1,8 + 0,5 = 2,3$$
6. $$8\cdot\sqrt{5\frac{1}{16}}+3 = 8\cdot\sqrt{\frac{81}{16}} + 3 = 8\cdot\sqrt{\left(\frac{9}{4}\right)^2} + 3 = 8\cdot\frac{9}{4} + 3 = 2\cdot 9 + 3 = 18 + 3 = 21$$

Ответ:

1. 14
2. 19
3. 1
4. 2
5. 2,3
6. 21