Упр.2.144 ГДЗ Дорофеев Суворова 8 класс (Алгебра)

а) (v28-3v5)-(v7+v20);
б) (3v32-2v18)+(v50-2v8);
в) (v27-3v45-v20)-(3v12-2v80);
г) (3v60-2v54)+(4v15+6v6-v600).

а) $$\left(\sqrt{28}-3\sqrt{5}\right)-\left(\sqrt{7}+\sqrt{20}\right)$$
$$=2\sqrt{7}-3\sqrt{5}-\sqrt{7}-2\sqrt{5}$$
$$=\sqrt{7}-5\sqrt{5}.$$

б) $$\left(3\sqrt{32}-2\sqrt{18}\right)+\left(\sqrt{50}-2\sqrt{8}\right)$$
$$=3\cdot 4\sqrt{2}-2\cdot 3\sqrt{2}+5\sqrt{2}-2\cdot 2\sqrt{2}$$
$$=12\sqrt{2}-6\sqrt{2}+5\sqrt{2}-4\sqrt{2}$$
$$=7\sqrt{2}.$$

в) $$\left(\sqrt{27}-3\sqrt{45}-\sqrt{20}\right)-\left(3\sqrt{12}-2\sqrt{80}\right)$$
$$=3\sqrt{3}-3\cdot 3\sqrt{5}-2\sqrt{5}-3\cdot 2\sqrt{3}+2\cdot 4\sqrt{5}$$
$$=3\sqrt{3}-9\sqrt{5}-2\sqrt{5}-6\sqrt{3}+8\sqrt{5}$$
$$=-3\sqrt{3}-3\sqrt{5}.$$

г) $$\left(3\sqrt{60}-2\sqrt{54}\right)+\left(4\sqrt{15}+6\sqrt{6}-\sqrt{600}\right)$$
$$=3\cdot 2\sqrt{15}-2\cdot 3\sqrt{6}+4\sqrt{15}+6\sqrt{6}-10\sqrt{6}$$
$$=6\sqrt{15}-6\sqrt{6}+4\sqrt{15}+6\sqrt{6}-10\sqrt{6}$$
$$=10\sqrt{15}-10\sqrt{6}.$$

Ответ

а) $$\sqrt{7}-5\sqrt{5}$$; б) $$7\sqrt{2}$$; в) $$-3\sqrt{3}-3\sqrt{5}$$; г) $$10\sqrt{15}-10\sqrt{6}$$.