Упр.17.18 ГДЗ Мерзляк Поляков 8 класс (Алгебра)

1) 3v8+v128-1/3 v162;
2) v5a-2v20a+3v80a;
3) v(c^5 )+4cv(c^3 )-5c^2 vc.

1) $$3\sqrt{8}+\sqrt{128}-\frac13\sqrt{162}=3\sqrt{4\cdot 2}+\sqrt{64\cdot 2}-\frac13\sqrt{81\cdot 2}$$

$$=3\cdot 2\sqrt{2}+8\sqrt{2}-\frac13\cdot 9\sqrt{2}=6\sqrt{2}+8\sqrt{2}-3\sqrt{2}=11\sqrt{2}.$$

2) $$\sqrt{5a}-2\sqrt{20a}+3\sqrt{80a}=\sqrt{5a}-2\sqrt{4\cdot 5a}+3\sqrt{16\cdot 5a}$$

$$=\sqrt{5a}-2\cdot 2\sqrt{5a}+3\cdot 4\sqrt{5a}=\sqrt{5a}-4\sqrt{5a}+12\sqrt{5a}=9\sqrt{5a}.$$

3) $$\sqrt{c^5}+4c\sqrt{c^3}-5c^2\sqrt{c}=\sqrt{c^4\cdot c}+4c\sqrt{c^2\cdot c}-5c^2\sqrt{c}$$

$$=c^2\sqrt{c}+4c\cdot c\sqrt{c}-5c^2\sqrt{c}=c^2\sqrt{c}+4c^2\sqrt{c}-5c^2\sqrt{c}=0.$$

Ответ

1) $$11\sqrt{2}$$; 2) $$9\sqrt{5a}$$; 3) $$0$$.