Упр.876 ГДЗ Никольский Потапов 9 класс (Алгебра)

в) v200-(1/2)·v32+2v72; г) (1/5)v300-(2/3)v27+v75.

1. а)

   $$\left(2\sqrt{38}-\sqrt{57}\right)\cdot \frac{2}{19}\cdot \sqrt{19}+\sqrt{12}$$
   $$=\left(2\sqrt{38}-\sqrt{57}\right)\cdot \frac{2}{\sqrt{19}}+2\sqrt{3}$$
   $$=4\sqrt{2}-2\sqrt{3}+2\sqrt{3}=4\sqrt{2}.$$

2. б)

   $$\left(\sqrt{14}-2\sqrt{35}\right)\cdot \frac{1}{7}\cdot \sqrt{7}+\sqrt{20}$$
   $$=\left(\sqrt{14}-2\sqrt{35}\right)\cdot \frac{1}{\sqrt{7}}+2\sqrt{5}$$
   $$=\sqrt{2}-2\sqrt{5}+2\sqrt{5}=\sqrt{2}.$$

3. в)

   $$\sqrt{200}-\frac{1}{2}\cdot \sqrt{32}+2\sqrt{72}$$
   $$=10\sqrt{2}-\frac{1}{2}\cdot 4\sqrt{2}+2\cdot 6\sqrt{2}$$
   $$=10\sqrt{2}-2\sqrt{2}+12\sqrt{2}=20\sqrt{2}.$$

4. г)

   $$\frac{1}{5}\sqrt{300}-\frac{2}{3}\sqrt{27}+\sqrt{75}$$
   $$=\frac{1}{5}\cdot 10\sqrt{3}-\frac{2}{3}\cdot 3\sqrt{3}+5\sqrt{3}$$
   $$=2\sqrt{3}-2\sqrt{3}+5\sqrt{3}=5\sqrt{3}.$$

Ответ

а) $$4\sqrt{2}$$; б) $$\sqrt{2}$$; в) $$20\sqrt{2}$$; г) $$5\sqrt{3}$$.