Решение задания 422

a) $$ \sqrt{8p} - \sqrt{2p} + \sqrt{18p} = \sqrt{4 \cdot 2p} - \sqrt{2p} + \sqrt{9 \cdot 2p} = 2\sqrt{2p} - \sqrt{2p} + 3\sqrt{2p} = (2 - 1 + 3)\sqrt{2p} = 4\sqrt{2p} $$

б) $$ \sqrt{160c} + 2\sqrt{40c} - 3\sqrt{90c} = \sqrt{16 \cdot 10c} + 2\sqrt{4 \cdot 10c} - 3\sqrt{9 \cdot 10c} = 4\sqrt{10c} + 2 \cdot 2\sqrt{10c} - 3 \cdot 3\sqrt{10c} = 4\sqrt{10c} + 4\sqrt{10c} - 9\sqrt{10c} = (4 + 4 - 9)\sqrt{10c} = -\sqrt{10c} $$

в) $$ 5\sqrt{27m} - 4\sqrt{48m} - 2\sqrt{12m} = 5\sqrt{9 \cdot 3m} - 4\sqrt{16 \cdot 3m} - 2\sqrt{4 \cdot 3m} = 5 \cdot 3\sqrt{3m} - 4 \cdot 4\sqrt{3m} - 2 \cdot 2\sqrt{3m} = 15\sqrt{3m} - 16\sqrt{3m} - 4\sqrt{3m} = (15 - 16 - 4)\sqrt{3m} = -5\sqrt{3m} $$

Ответ:

а) $$4\sqrt{2p}$$

б) $$\sqrt{10c}$$

в) $$-5\sqrt{3m}$$