Решение:

1. $$(\sqrt{12} + \sqrt{27})\sqrt{3} = (\sqrt{4 \cdot 3} + \sqrt{9 \cdot 3})\sqrt{3} = (2\sqrt{3} + 3\sqrt{3})\sqrt{3} = 5\sqrt{3} \cdot \sqrt{3} = 5 \cdot 3 = 15$$

   Ответ: 15

2. $$(\sqrt{8} - \sqrt{72})\sqrt{2} = (\sqrt{4 \cdot 2} - \sqrt{36 \cdot 2})\sqrt{2} = (2\sqrt{2} - 6\sqrt{2})\sqrt{2} = -4\sqrt{2} \cdot \sqrt{2} = -4 \cdot 2 = -8$$

   Ответ: -8

3. $$3\sqrt{5} + (\sqrt{75} - \sqrt{15})\sqrt{3} = 3\sqrt{5} + (\sqrt{25 \cdot 3} - \sqrt{15})\sqrt{3} = 3\sqrt{5} + (5\sqrt{3} - \sqrt{15})\sqrt{3} = 3\sqrt{5} + 5 \cdot 3 - \sqrt{45} = 3\sqrt{5} + 15 - \sqrt{9 \cdot 5} = 3\sqrt{5} + 15 - 3\sqrt{5} = 15$$

   Ответ: 15

4. $$(\sqrt{60} - \sqrt{45})\sqrt{5} - 10\sqrt{3} = (\sqrt{4 \cdot 15} - \sqrt{9 \cdot 5})\sqrt{5} - 10\sqrt{3} = (2\sqrt{15} - 3\sqrt{5})\sqrt{5} - 10\sqrt{3} = 2\sqrt{75} - 3 \cdot 5 - 10\sqrt{3} = 2\sqrt{25 \cdot 3} - 15 - 10\sqrt{3} = 2 \cdot 5\sqrt{3} - 15 - 10\sqrt{3} = 10\sqrt{3} - 15 - 10\sqrt{3} = -15$$

   Ответ: -15

5. $$(\sqrt{200} + 5\sqrt{20})\sqrt{5} - \sqrt{1000} = (\sqrt{100 \cdot 2} + 5\sqrt{4 \cdot 5})\sqrt{5} - \sqrt{100 \cdot 10} = (10\sqrt{2} + 5 \cdot 2\sqrt{5})\sqrt{5} - 10\sqrt{10} = (10\sqrt{2} + 10\sqrt{5})\sqrt{5} - 10\sqrt{10} = 10\sqrt{10} + 10 \cdot 5 - 10\sqrt{10} = 50$$

   Ответ: 50

6. $$(\sqrt{300} - 6\sqrt{50})\sqrt{2} - \sqrt{600} = (\sqrt{100 \cdot 3} - 6\sqrt{25 \cdot 2})\sqrt{2} - \sqrt{100 \cdot 6} = (10\sqrt{3} - 6 \cdot 5\sqrt{2})\sqrt{2} - 10\sqrt{6} = (10\sqrt{3} - 30\sqrt{2})\sqrt{2} - 10\sqrt{6} = 10\sqrt{6} - 30 \cdot 2 - 10\sqrt{6} = -60$$

   Ответ: -60