Упрощение выражений

1. $$5\sqrt{3}-\sqrt{27} = 5\sqrt{3}-\sqrt{9\times 3} = 5\sqrt{3}-3\sqrt{3} = 2\sqrt{3}$$

   Ответ: $$2\sqrt{3}$$

2. $$\sqrt{18}+5\sqrt{2} = \sqrt{9\times 2}+5\sqrt{2} = 3\sqrt{2}+5\sqrt{2} = 8\sqrt{2}$$

   Ответ: $$8\sqrt{2}$$

3. $$\frac{1}{5}\sqrt{125}+2\sqrt{45} = \frac{1}{5}\sqrt{25\times 5}+2\sqrt{9\times 5} = \frac{1}{5}\times 5\sqrt{5}+2\times 3\sqrt{5} = \sqrt{5}+6\sqrt{5} = 7\sqrt{5}$$

   Ответ: $$7\sqrt{5}$$

4. $$3\sqrt{45}-\frac{1}{2}\sqrt{20} = 3\sqrt{9\times 5}-\frac{1}{2}\sqrt{4\times 5} = 3\times 3\sqrt{5}-\frac{1}{2}\times 2\sqrt{5} = 9\sqrt{5}-\sqrt{5} = 8\sqrt{5}$$

   Ответ: $$8\sqrt{5}$$

5. $$0.5\sqrt{24}-\frac{1}{3}\sqrt{54} = 0.5\sqrt{4\times 6}-\frac{1}{3}\sqrt{9\times 6} = 0.5\times 2\sqrt{6}-\frac{1}{3}\times 3\sqrt{6} = \sqrt{6}-\sqrt{6} = 0$$

   Ответ: $$0$$

6. $$0.8\sqrt{50}+\frac{1}{4}\sqrt{32} = 0.8\sqrt{25\times 2}+\frac{1}{4}\sqrt{16\times 2} = 0.8\times 5\sqrt{2}+\frac{1}{4}\times 4\sqrt{2} = 4\sqrt{2}+\sqrt{2} = 5\sqrt{2}$$

   Ответ: $$5\sqrt{2}$$