Упр.15.19 Часть 1 ГДЗ Мордкович Семенов 9 класс (Алгебра)

а) 2v32+v50-0,5v72;
б) 4v252-5v112+v175;
в) 5v48-4v3-v243;
г) 3v726-4v486-2v294.

1. $$2\sqrt{32}+\sqrt{50}-0{,}5\sqrt{72}$$

   $$=2\sqrt{16\cdot 2}+\sqrt{25\cdot 2}-0{,}5\sqrt{36\cdot 2}$$

   $$=2\cdot 4\sqrt{2}+5\sqrt{2}-0{,}5\cdot 6\sqrt{2}$$

   $$=8\sqrt{2}+5\sqrt{2}-3\sqrt{2}=10\sqrt{2}$$

2. $$4\sqrt{252}-5\sqrt{112}+\sqrt{175}$$

   $$=4\sqrt{36\cdot 7}-5\sqrt{16\cdot 7}+\sqrt{25\cdot 7}$$

   $$=4\cdot 6\sqrt{7}-5\cdot 4\sqrt{7}+5\sqrt{7}$$

   $$=24\sqrt{7}-20\sqrt{7}+5\sqrt{7}=9\sqrt{7}$$

3. $$5\sqrt{48}-4\sqrt{3}-\sqrt{243}$$

   $$=5\sqrt{16\cdot 3}-4\sqrt{3}-\sqrt{81\cdot 3}$$

   $$=5\cdot 4\sqrt{3}-4\sqrt{3}-9\sqrt{3}$$

   $$=20\sqrt{3}-4\sqrt{3}-9\sqrt{3}=7\sqrt{3}$$

4. $$3\sqrt{726}-4\sqrt{486}-2\sqrt{294}$$

   $$=3\sqrt{121\cdot 6}-4\sqrt{81\cdot 6}-2\sqrt{49\cdot 6}$$

   $$=3\cdot 11\sqrt{6}-4\cdot 9\sqrt{6}-2\cdot 7\sqrt{6}$$

   $$=33\sqrt{6}-36\sqrt{6}-14\sqrt{6}=-17\sqrt{6}$$

Ответ

а) $$10\sqrt{2}$$; б) $$9\sqrt{7}$$; в) $$7\sqrt{3}$$; г) $$-17\sqrt{6}$$.