Упростите выражение:
а) $\sqrt{8p} - \sqrt{2p} + \sqrt{18p}$;
б) $3\sqrt{160c} + 2\sqrt{40c} - 3\sqrt{90c}$;
в) $5\sqrt{27m} - 4\sqrt{48m} - 2\sqrt{12m}$;
г) $\sqrt{54} - \sqrt{24} + \sqrt{150}$;
д) $3\sqrt{2} + \sqrt{32} - \sqrt{200}$;
е) $2\sqrt{72} - \sqrt{50} - 2\sqrt{8}$.
$\sqrt{8p} - \sqrt{2p} + \sqrt{18p} = \sqrt{4 * 2p} - \sqrt{2p} + \sqrt{9 * 2p} = 2\sqrt{2p} - \sqrt{2p} + 3\sqrt{2p} = (2 - 1 + 3)\sqrt{2p} = 4\sqrt{2p}$
$3\sqrt{160c} + 2\sqrt{40c} - 3\sqrt{90c} = \sqrt{16 * 10c} + 2\sqrt{4 * 10c} - 3\sqrt{9 * 10c} = 4\sqrt{10c} + 2 * 2\sqrt{10c} - 3 * 3\sqrt{10c} = (4 + 4 - 9)\sqrt{10c} = -\sqrt{10c}$
$5\sqrt{27m} - 4\sqrt{48m} - 2\sqrt{12m} = 5\sqrt{9 * 3m} - 4\sqrt{16 * 3m} - 2\sqrt{4 * 3m} = 5 * 3\sqrt{3m} - 4 * 4\sqrt{3m} - 2 * 2\sqrt{3m} = (15 - 16 - 4)\sqrt{3m} = -5\sqrt{3m}$
$\sqrt{54} - \sqrt{24} + \sqrt{150} = \sqrt{9 * 6} - \sqrt{4 * 6} + \sqrt{25 * 6} = 3\sqrt{6} - 2\sqrt{6} + 5\sqrt{6} = (3 - 2 + 5)\sqrt{6} = 6\sqrt{6}$
$3\sqrt{2} + \sqrt{32} - \sqrt{200} = 3\sqrt{2} + \sqrt{16 * 2} - \sqrt{100 * 2} = 3\sqrt{2} + 4\sqrt{2} - 10\sqrt{2} = (3 + 4 - 10)\sqrt{2} = -3\sqrt{2}$
$2\sqrt{72} - \sqrt{50} - 2\sqrt{8} = 2\sqrt{36 * 2} - \sqrt{25 * 2} - 2\sqrt{4 * 2} = 2 * 6\sqrt{2} - 5\sqrt{2} - 2 * 2\sqrt{2} = (12 - 5 - 4)\sqrt{2} = 3\sqrt{2}$
Пожауйста, оцените решение
