Question

Упростите выражение:
1. (√18+√72)•√2;
2. (4√3-√75+4)•3√3;
3. (√600+√6-√24)•√6.

Answer 1

1) $\displaystyle \tt (\sqrt{18}+\sqrt{72})\cdot\sqrt{2}=(3\sqrt{2}+6\sqrt{2})\cdot\sqrt{2}=9\sqrt{2}\cdot\sqrt{2}=9\cdot2=\bold{18}$

2) $\displaystyle \tt (4\sqrt{3}-\sqrt{75}+4)\cdot3\sqrt{3}=(4\sqrt{3}-5\sqrt{3}+4)\cdot3\sqrt{3}=(-\sqrt{3}+4)\cdot3\sqrt{3}=\bold{-9+12\sqrt{3}}$

3) $\displaystyle \tt (\displaystyle \tt \sqrt{600}+\sqrt{6}-\sqrt{24})\cdot\sqrt{6}=(10\sqrt{6}+\sqrt{6}-2\sqrt{6})\cdot\sqrt{6}=9\sqrt{6}\cdot\sqrt{6}=9\cdot6=\bold{54}$