№ 6. Упростите выражение: a) (10\sqrt{3}-4\sqrt{48}-\sqrt{75}) б) ((5\sqrt{2}-\sqrt{18})\sqrt{2}) в) ((3-\sqrt{2})^2) г) (2\sqrt{2}+\sqrt{50}-\sqrt{98}) д) ((3\sqrt{5}-\sqrt{20})\sqrt{5}) е) ((-\sqrt{3}+\sqrt{2})^2)

Решение №6: a) (10\sqrt{3}-4\sqrt{48}-\sqrt{75} = 10\sqrt{3}-4\sqrt{16\cdot3}-\sqrt{25\cdot3} = 10\sqrt{3}-4\cdot4\sqrt{3}-5\sqrt{3} = 10\sqrt{3}-16\sqrt{3}-5\sqrt{3} = (10-16-5)\sqrt{3} = -11\sqrt{3}) б) ((5\sqrt{2}-\sqrt{18})\sqrt{2} = (5\sqrt{2}-\sqrt{9\cdot2})\sqrt{2} = (5\sqrt{2}-3\sqrt{2})\sqrt{2} = 2\sqrt{2}\cdot\sqrt{2} = 2\cdot2 = 4) в) ((3-\sqrt{2})^2 = 3^2 - 2\cdot3\cdot\sqrt{2} + (\sqrt{2})^2 = 9 - 6\sqrt{2} + 2 = 11 - 6\sqrt{2}) г) (2\sqrt{2}+\sqrt{50}-\sqrt{98} = 2\sqrt{2}+\sqrt{25\cdot2}-\sqrt{49\cdot2} = 2\sqrt{2}+5\sqrt{2}-7\sqrt{2} = (2+5-7)\sqrt{2} = 0\sqrt{2} = 0) д) ((3\sqrt{5}-\sqrt{20})\sqrt{5} = (3\sqrt{5}-\sqrt{4\cdot5})\sqrt{5} = (3\sqrt{5}-2\sqrt{5})\sqrt{5} = \sqrt{5}\cdot\sqrt{5} = 5) е) ((-\sqrt{3}+\sqrt{2})^2 = (-\sqrt{3})^2 + 2(-\sqrt{3})(\sqrt{2})+(\sqrt{2})^2 = 3 - 2\sqrt{6} + 2 = 5 - 2\sqrt{6})