Упр.19.23 ГДЗ Мерзляк Поляков 8 класс (Алгебра)

1) 10v3-5v48+2v75; 2) (3v5-v20) v5; 3) (5-v2)^2.

1. $$10\sqrt{3}-5\sqrt{48}+2\sqrt{75}=10\sqrt{3}-5\sqrt{16\cdot 3}+2\sqrt{25\cdot 3}$$
   $$=10\sqrt{3}-5\cdot 4\sqrt{3}+2\cdot 5\sqrt{3}=10\sqrt{3}-20\sqrt{3}+10\sqrt{3}=0.$$

2. $$(3\sqrt{5}-\sqrt{20})\sqrt{5}=(3\sqrt{5}-\sqrt{4\cdot 5})\sqrt{5}=(3\sqrt{5}-2\sqrt{5})\sqrt{5}$$
   $$=\sqrt{5}\cdot \sqrt{5}=5.$$

3. $$(5-\sqrt{2})^2=5^2-2\cdot 5\sqrt{2}+(\sqrt{2})^2=25-10\sqrt{2}+2=27-10\sqrt{2}.$$

Ответ

1) $$0$$; 2) $$5$$; 3) $$27-10\sqrt{2}$$.