Question

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

Answer 1

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

2) $displaystyle tt (4sqrt{3}-sqrt{75}+4)cdot3sqrt{3}=(4sqrt{3}-5sqrt{3}+4)cdot3sqrt{3}=(-sqrt{3}+4)cdot3sqrt{3}=bold{-9+12sqrt{3}}$

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