Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 401

а) 1/2$$\sqrt{24}$$ = 1/2$$\sqrt{4 ⋅ 6}$$ = 1/2$$\sqrt{2²}$$ ⋅ $$\sqrt{6}$$ = 0,5 ⋅ 2 ⋅ $$\sqrt{6}$$ = $$\sqrt{6}$$
б) 2/3$$\sqrt{45}$$ = 2/3$$\sqrt{9 ⋅ 5}$$ = 2/3$$\sqrt{3²}$$ ⋅ $$\sqrt{5}$$ = 2/3 ⋅ 3 ⋅ $$\sqrt{5}$$ = 2 ⋅ 3 : 3/3 : 3$$\sqrt{5}$$ = 2$$\sqrt{5}$$
в) −1/7$$\sqrt{147}$$ = −1/7$$\sqrt{49 ⋅ 3}$$ = −1/7$$\sqrt{7²}$$ ⋅ $$\sqrt{3}$$ = −1/7 ⋅ 7 ⋅ $$\sqrt{3}$$ = −1 ⋅ 7 : 7/7 : 7$$\sqrt{3}$$ = −$$\sqrt{3}$$
г) −1/5$$\sqrt{275}$$ = −1/5$$\sqrt{25 ⋅ 11}$$ = −1/5$$\sqrt{5²}$$ ⋅ $$\sqrt{11}$$ = −1/5 ⋅ 5 ⋅ $$\sqrt{11}$$ = −1 ⋅ 5 : 5/5 : 5$$\sqrt{11}$$ = −$$\sqrt{11}$$
д) 0,1$$\sqrt{20000}$$ = 0,1$$\sqrt{10000 ⋅ 2}$$ = 0,1$$\sqrt{100²}$$ ⋅ $$\sqrt{2}$$ = 0,1 ⋅ 100 ⋅ $$\sqrt{2}$$ = 10$$\sqrt{2}$$
е) −0,05$$\sqrt{28800}$$ = −0,05$$\sqrt{144 ⋅ 100 ⋅ 2}$$ = −0,05$$\sqrt{12²}$$ ⋅ $$\sqrt{10²}$$ ⋅ $$\sqrt{2}$$ = −0,05 ⋅ 12 ⋅ 10 ⋅ $$\sqrt{2}$$ = −6$$\sqrt{2}$$