Упр.16.28 ГДЗ Мордкович 8 класс (Алгебра)

• а) $$(6\sqrt{12}-\sqrt{75})\cdot\sqrt{3}$$; б) $$(3\sqrt{5}-2\sqrt{20})\cdot\sqrt{5}$$; в) $$(\sqrt{32}+2\sqrt{18})\cdot\sqrt{2}$$; г) $$(2\sqrt{50}-5\sqrt{2})\cdot\sqrt{2}$$.

1. $$\left(6\sqrt{12}-\sqrt{75}\right)\cdot \sqrt{3}$$
   $$= \left(6\cdot 2\sqrt{3}-5\sqrt{3}\right)\cdot \sqrt{3}$$
   $$= \left(12\sqrt{3}-5\sqrt{3}\right)\cdot \sqrt{3}$$
   $$= 7\sqrt{3}\cdot \sqrt{3}=7\cdot 3=21.$$

2. $$\left(3\sqrt{5}-2\sqrt{20}\right)\cdot \sqrt{5}$$
   $$= \left(3\sqrt{5}-2\cdot 2\sqrt{5}\right)\cdot \sqrt{5}$$
   $$= \left(3\sqrt{5}-4\sqrt{5}\right)\cdot \sqrt{5}$$
   $$= -\sqrt{5}\cdot \sqrt{5}=-5.$$

3. $$\left(\sqrt{32}+2\sqrt{18}\right)\cdot \sqrt{2}$$
   $$= \left(4\sqrt{2}+2\cdot 3\sqrt{2}\right)\cdot \sqrt{2}$$
   $$= \left(4\sqrt{2}+6\sqrt{2}\right)\cdot \sqrt{2}$$
   $$= 10\sqrt{2}\cdot \sqrt{2}=10\cdot 2=20.$$

4. $$\left(2\sqrt{50}-5\sqrt{2}\right)\cdot \sqrt{2}$$
   $$= \left(2\cdot 5\sqrt{2}-5\sqrt{2}\right)\cdot \sqrt{2}$$
   $$= \left(10\sqrt{2}-5\sqrt{2}\right)\cdot \sqrt{2}$$
   $$= 5\sqrt{2}\cdot \sqrt{2}=5\cdot 2=10.$$

Ответ

а) $$21$$; б) $$-5$$; в) $$20$$; г) $$10$$.