ДЗ алгебра на 12-01-26: 1. Упростите выражение: 1) a) 3√C+8Vc-9vc; 6) 5va-2V6+√a; 2) a) в) 4х+64x-V81x; г) √27-√48+√75; 12y-0,548y+2108y; б) 2/8a+0,345c-418a+0,01 √500c; 3) a) √3 (√27-V48); в) 3/2(2-5/32)-2/18; 6) (5√7-√63+√14) √7; г) √12-(√15-3√5)√5.

1. Упростите выражение:

1) a) $$3\sqrt{c}+8\sqrt{c}-9\sqrt{c} = (3+8-9)\sqrt{c} = 2\sqrt{c}$$.

Ответ: $$2\sqrt{c}$$

б) $$5\sqrt{a}-2\sqrt{b}+\sqrt{a} = (5+1)\sqrt{a}-2\sqrt{b} = 6\sqrt{a}-2\sqrt{b}$$.

Ответ: $$6\sqrt{a}-2\sqrt{b}$$

в) $$\sqrt{4x}+\sqrt{64x}-\sqrt{81x} = 2\sqrt{x}+8\sqrt{x}-9\sqrt{x} = (2+8-9)\sqrt{x} = \sqrt{x}$$.

Ответ: $$\sqrt{x}$$

г) $$\sqrt{27}-\sqrt{48}+\sqrt{75} = \sqrt{9\cdot3}-\sqrt{16\cdot3}+\sqrt{25\cdot3} = 3\sqrt{3}-4\sqrt{3}+5\sqrt{3} = (3-4+5)\sqrt{3} = 4\sqrt{3}$$.

Ответ: $$4\sqrt{3}$$

2) а) $$\sqrt{12y}-0.5\sqrt{48y}+2\sqrt{108y} = \sqrt{4\cdot3y}-0.5\sqrt{16\cdot3y}+2\sqrt{36\cdot3y} = 2\sqrt{3y}-0.5\cdot4\sqrt{3y}+2\cdot6\sqrt{3y} = 2\sqrt{3y}-2\sqrt{3y}+12\sqrt{3y} = 12\sqrt{3y}$$.

Ответ: $$12\sqrt{3y}$$

б) $$2\sqrt{8a}+0.3\sqrt{45c}-4\sqrt{18a}+0.01\sqrt{500c} = 2\sqrt{4\cdot2a}+0.3\sqrt{9\cdot5c}-4\sqrt{9\cdot2a}+0.01\sqrt{100\cdot5c} = 2\cdot2\sqrt{2a}+0.3\cdot3\sqrt{5c}-4\cdot3\sqrt{2a}+0.01\cdot10\sqrt{5c} = 4\sqrt{2a}+0.9\sqrt{5c}-12\sqrt{2a}+0.1\sqrt{5c} = -8\sqrt{2a}+1\sqrt{5c} = -8\sqrt{2a}+\sqrt{5c}$$.

Ответ: $$-8\sqrt{2a}+\sqrt{5c}$$

3) a) $$\sqrt{3}(\sqrt{27}-\sqrt{48}) = \sqrt{3}(\sqrt{9\cdot3}-\sqrt{16\cdot3}) = \sqrt{3}(3\sqrt{3}-4\sqrt{3}) = \sqrt{3}(-\sqrt{3}) = -3$$.

Ответ: $$-3$$

в) $$3\sqrt{2}(2-5\sqrt{32})-2\sqrt{18} = 3\sqrt{2}(2-5\sqrt{16\cdot2})-2\sqrt{9\cdot2} = 3\sqrt{2}(2-5\cdot4\sqrt{2})-2\cdot3\sqrt{2} = 3\sqrt{2}(2-20\sqrt{2})-6\sqrt{2} = 6\sqrt{2}-60\cdot2-6\sqrt{2} = -120$$.

Ответ: $$-120$$

6) $$(5\sqrt{7}-\sqrt{63}+\sqrt{14})\cdot\sqrt{7} = (5\sqrt{7}-\sqrt{9\cdot7}+\sqrt{14})\cdot\sqrt{7} = (5\sqrt{7}-3\sqrt{7}+\sqrt{14})\cdot\sqrt{7} = (2\sqrt{7}+\sqrt{14})\cdot\sqrt{7} = 2\cdot7+\sqrt{14\cdot7} = 14+\sqrt{2\cdot7\cdot7} = 14+7\sqrt{2}$$.

Ответ: $$14+7\sqrt{2}$$

г) $$\sqrt{12}-(\sqrt{15}-3\sqrt{5})\sqrt{5} = \sqrt{4\cdot3}-(\sqrt{15\cdot5}-3\cdot5) = 2\sqrt{3}-(\sqrt{3\cdot5\cdot5}-15) = 2\sqrt{3}-(5\sqrt{3}-15) = 2\sqrt{3}-5\sqrt{3}+15 = -3\sqrt{3}+15 = 15-3\sqrt{3}$$.

Ответ: $$15-3\sqrt{3}$$