12 Упростите выражение: a) 5√3-2√3; б) 3√5⋅4√20; в) (2√5)²/10; г) √8/√50; д) 2√10⋅√2/√80

а) $$5√3 - 2√3 = (5-2)√3 = 3√3$$.

б) $$3√5 \cdot 4√20 = 3 \cdot 4 \cdot √5 \cdot √20 = 12 \cdot √{5 \cdot 20} = 12 \cdot √{100} = 12 \cdot 10 = 120$$.

в) $$\frac{(2√5)^2}{10} = \frac{2^2 \cdot (√5)^2}{10} = \frac{4 \cdot 5}{10} = \frac{20}{10} = 2$$.

г) $$\frac{√8}{√50} = √{\frac{8}{50}} = √{\frac{4}{25}} = \frac{√4}{√25} = \frac{2}{5}$$.

д) $$\frac{2√{10} \cdot √2}{√{80}} = \frac{2√{10 \cdot 2}}{√{80}} = \frac{2√{20}}{√{80}} = 2√{\frac{20}{80}} = 2√{\frac{1}{4}} = 2 \cdot \frac{1}{2} = 1$$.

Ответ: а) $$3√3$$, б) $$120$$, в) $$2$$, г) $$\frac{2}{5}$$, д) $$1$$