22. Упростите выражение: а) √(8p) − √(2p) + √(18p); б) √(160c) + 2√(40c) − 3√(90c); в) 5√(27m) − 4√(48m) − 2√(12m); г) √54 − √24 + √150; д) 3√2 + √32 − √200; е) 2√72 − √50 − 2√8.

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Вопрос:

Accepted Answer

а) Выносим полные квадраты из-под корней: \(\sqrt{8p}=2\sqrt{2p}\), \(\sqrt{18p}=3\sqrt{2p}\).
\(2\sqrt{2p}-\sqrt{2p}+3\sqrt{2p}=4\sqrt{2p}\).
б) \(\sqrt{160c}=4\sqrt{10c}\), \(\sqrt{40c}=2\sqrt{10c}\), \(\sqrt{90c}=3\sqrt{10c}\).
\(4\sqrt{10c}+2\cdot2\sqrt{10c}-3\cdot3\sqrt{10c}=(4+4-9)\sqrt{10c}=-\sqrt{10c}\).
в) \(\sqrt{27m}=3\sqrt{3m}\), \(\sqrt{48m}=4\sqrt{3m}\), \(\sqrt{12m}=2\sqrt{3m}\).
\(5\cdot3\sqrt{3m}-4\cdot4\sqrt{3m}-2\cdot2\sqrt{3m}=(15-16-4)\sqrt{3m}=-5\sqrt{3m}\).
г) \(\sqrt{54}=3\sqrt6\), \(\sqrt{24}=2\sqrt6\), \(\sqrt{150}=5\sqrt6\).
\(3\sqrt6-2\sqrt6+5\sqrt6=6\sqrt6\).
д) \(\sqrt{32}=4\sqrt2\), \(\sqrt{200}=10\sqrt2\).
\(3\sqrt2+4\sqrt2-10\sqrt2=-3\sqrt2\).
е) \(\sqrt{72}=6\sqrt2\), \(\sqrt{50}=5\sqrt2\), \(\sqrt8=2\sqrt2\).
\(2\cdot6\sqrt2-5\sqrt2-2\cdot2\sqrt2=(12-5-4)\sqrt2=3\sqrt2\).

Ответ: а) \(4\sqrt{2p}\); б) \(-\sqrt{10c}\); в) \(-5\sqrt{3m}\); г) \(6\sqrt6\); д) \(-3\sqrt2\); е) \(3\sqrt2\).