1. Упростите выражение: 1) а) 2√a + 6√a - 7√a;

### 1. Упростите выражение: **1) а)** $2\sqrt{a} + 6\sqrt{a} - 7\sqrt{a} = (2 + 6 - 7)\sqrt{a} = \sqrt{a}$ **б)** $4\sqrt{x} + 2\sqrt{x} - 5\sqrt{x} = (4 + 2 - 5)\sqrt{x} = \sqrt{x}$ **в)** $\sqrt{49c} - \sqrt{16c} + \sqrt{25c} = 7\sqrt{c} - 4\sqrt{c} + 5\sqrt{c} = (7 - 4 + 5)\sqrt{c} = 8\sqrt{c}$ **г)** $\sqrt{32} + \sqrt{18} - \sqrt{50} = \sqrt{16 \cdot 2} + \sqrt{9 \cdot 2} - \sqrt{25 \cdot 2} = 4\sqrt{2} + 3\sqrt{2} - 5\sqrt{2} = (4 + 3 - 5)\sqrt{2} = 2\sqrt{2}$ **2) а)** $\sqrt{8m} - 0,2\sqrt{200m} + 3\sqrt{72m} = 2\sqrt{2m} - 0,2 \cdot 10\sqrt{2m} + 3 \cdot 6\sqrt{2m} = 2\sqrt{2m} - 2\sqrt{2m} + 18\sqrt{2m} = 18\sqrt{2m}$ **б)** $3\sqrt{12b} + 0,5\sqrt{108k} - 2\sqrt{48b} + 0,01\sqrt{300k} = 3 \cdot 2\sqrt{3b} + 0,5 \cdot 6\sqrt{3k} - 2 \cdot 4\sqrt{3b} + 0,01 \cdot 10\sqrt{3k} = 6\sqrt{3b} + 3\sqrt{3k} - 8\sqrt{3b} + 0,1\sqrt{3k} = -2\sqrt{3b} + 3,1\sqrt{3k}$ **3) а)** $\sqrt{6}(\sqrt{24} - \sqrt{54}) = \sqrt{6} \cdot \sqrt{24} - \sqrt{6} \cdot \sqrt{54} = \sqrt{144} - \sqrt{324} = 12 - 18 = -6$ **б)** $(7\sqrt{2} - \sqrt{98} + \sqrt{10}) \cdot \sqrt{2} = (7\sqrt{2} - 7\sqrt{2} + \sqrt{10}) \cdot \sqrt{2} = \sqrt{10} \cdot \sqrt{2} = \sqrt{20} = 2\sqrt{5}$ **в)** $2\sqrt{3}(3 - 4\sqrt{75}) - 3\sqrt{12} = 2\sqrt{3} \cdot 3 - 2\sqrt{3} \cdot 4 \cdot 5\sqrt{3} - 3 \cdot 2\sqrt{3} = 6\sqrt{3} - 40 \cdot 3 - 6\sqrt{3} = -120$ **г)** $\sqrt{18} - (\sqrt{14} - 2\sqrt{7}) \cdot \sqrt{7} = 3\sqrt{2} - (\sqrt{98} - 2 \cdot 7) = 3\sqrt{2} - 7\sqrt{2} + 14 = 14 - 4\sqrt{2}$ ### 2. Выполните действия: **1) а)** $(1 - \sqrt{2})(3 + \sqrt{2}) = 3 + \sqrt{2} - 3\sqrt{2} - 2 = 1 - 2\sqrt{2}$ **б)** $(\sqrt{3} + \sqrt{7})(2\sqrt{3} - \sqrt{7}) = 2 \cdot 3 - \sqrt{21} + 2\sqrt{21} - 7 = 6 + \sqrt{21} - 7 = \sqrt{21} - 1$ **в)** $(\sqrt{5} - \sqrt{18})(\sqrt{5} - 2\sqrt{2}) = (\sqrt{5} - 3\sqrt{2})(\sqrt{5} - 2\sqrt{2}) = 5 - 2\sqrt{10} - 3\sqrt{10} + 6 \cdot 2 = 5 - 5\sqrt{10} + 12 = 17 - 5\sqrt{10}$ **г)** $(2\sqrt{7} + \sqrt{12})(\sqrt{12} - \sqrt{7}) - \sqrt{84} = (2\sqrt{7} + 2\sqrt{3})(2\sqrt{3} - \sqrt{7}) - 2\sqrt{21} = 4\sqrt{21} - 2 \cdot 7 + 4 \cdot 3 - 2\sqrt{21} - 2\sqrt{21} = 12 - 14 = -2$