Задание 3 Параграф 17 ГДЗ Рабочая тетрадь 2 Мерзляк Полонский 8 класс (Алгебра)

1) v81a+v16a-v121a;
2) v100c-v400c+v900c;
3) v45+v80-v500;
4) v8+v50-v18;
5) v150p-v54p+v24p;
6) v396m+2v44m-15v176m.

1. $$\sqrt{81a}+\sqrt{16a}-\sqrt{121a}=9\sqrt{a}+4\sqrt{a}-11\sqrt{a}=2\sqrt{a}$$
2. $$\sqrt{100c}-\sqrt{400c}+\sqrt{900c}=10\sqrt{c}-20\sqrt{c}+30\sqrt{c}=20\sqrt{c}$$
3. $$\sqrt{45}+\sqrt{80}-\sqrt{500}=\sqrt{9\cdot 5}+\sqrt{16\cdot 5}-\sqrt{100\cdot 5}$$
   $$=3\sqrt{5}+4\sqrt{5}-10\sqrt{5}=-3\sqrt{5}$$
4. $$\sqrt{8}+\sqrt{50}-\sqrt{18}=\sqrt{4\cdot 2}+\sqrt{25\cdot 2}-\sqrt{9\cdot 2}$$
   $$=2\sqrt{2}+5\sqrt{2}-3\sqrt{2}=4\sqrt{2}$$
5. $$\sqrt{150p}-\sqrt{54p}+\sqrt{24p}=\sqrt{25\cdot 6p}-\sqrt{9\cdot 6p}+\sqrt{4\cdot 6p}$$
   $$=5\sqrt{6p}-3\sqrt{6p}+2\sqrt{6p}=4\sqrt{6p}$$
6. $$\sqrt{396m}+2\sqrt{44m}-15\sqrt{176m}=\sqrt{36\cdot 11m}+2\sqrt{4\cdot 11m}-15\sqrt{16\cdot 11m}$$
   $$=6\sqrt{11m}+2\cdot 2\sqrt{11m}-15\cdot 4\sqrt{11m}$$
   $$=6\sqrt{11m}+4\sqrt{11m}-60\sqrt{11m}=-50\sqrt{11m}$$

Ответ

1) $$2\sqrt{a}$$; 2) $$20\sqrt{c}$$; 3) $$-3\sqrt{5}$$; 4) $$4\sqrt{2}$$; 5) $$4\sqrt{6p}$$; 6) $$-50\sqrt{11m}$$.