Упр.533 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1. $$\sqrt{18\cdot 200}=\sqrt{3600}=60$$
   $$\sqrt{3{,}6\cdot 0{,}4}=\sqrt{1{,}44}=1{,}2$$
   $$\sqrt{14{,}4\cdot 0{,}9}=\sqrt{12{,}96}=3{,}6$$
   $$\sqrt{13\cdot 52}=\sqrt{676}=26$$
   $$\sqrt{12{,}5\cdot 32}=\sqrt{400}=20$$
   $$\sqrt{108\cdot 27}=\sqrt{2916}=54$$
2. $$8\sqrt{2}-\sqrt{32}=8\sqrt{2}-\sqrt{16\cdot 2}=8\sqrt{2}-4\sqrt{2}=4\sqrt{2}$$
   $$6\sqrt{3}-\sqrt{27}=6\sqrt{3}-\sqrt{9\cdot 3}=6\sqrt{3}-3\sqrt{3}=3\sqrt{3}$$
   $$\sqrt{96}-3\sqrt{6}=\sqrt{16\cdot 6}-3\sqrt{6}=4\sqrt{6}-3\sqrt{6}=\sqrt{6}$$
   $$2\sqrt{500}-8\sqrt{5}=2\sqrt{100\cdot 5}-8\sqrt{5}=2\cdot 10\sqrt{5}-8\sqrt{5}=12\sqrt{5}$$
   $$5\sqrt{7}-\sqrt{700}-0{,}5\sqrt{28}=5\sqrt{7}-\sqrt{7\cdot 100}-0{,}5\sqrt{7\cdot 4}$$
   $$=5\sqrt{7}-10\sqrt{7}-0{,}5\cdot 2\sqrt{7}=-5\sqrt{7}-\sqrt{7}=-6\sqrt{7}$$
   $$2\sqrt{20}-\frac{1}{3}\sqrt{45}-0{,}6\sqrt{125}=2\sqrt{4\cdot 5}-\frac{1}{3}\sqrt{9\cdot 5}-0{,}6\sqrt{25\cdot 5}$$
   $$=2\cdot 2\sqrt{5}-\frac{1}{3}\cdot 3\sqrt{5}-0{,}6\cdot 5\sqrt{5}=4\sqrt{5}-\sqrt{5}-3\sqrt{5}=0$$

Ответ

1) $$60$$; $$1{,}2$$; $$3{,}6$$; $$26$$; $$20$$; $$54$$.

2) $$4\sqrt{2}$$; $$3\sqrt{3}$$; $$\sqrt{6}$$; $$12\sqrt{5}$$; $$-6\sqrt{7}$$; $$0$$.