Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 475

а) $$\sqrt{4³}$$ = $$\sqrt{(2²)³}$$ = $$\sqrt{(2³)²}$$ = |2³| = 2³ = 8
б) $$\sqrt{9⁵}$$ = $$\sqrt{(3²)⁵}$$ = $$\sqrt{(3⁵)²}$$ = |3⁵| = 3⁵ = 243
в) $$\sqrt{16⁵}$$ = $$\sqrt{(4²)⁵}$$ = $$\sqrt{(4⁵)²}$$ = |4⁵| = 4⁵ = 1024
г) $$\sqrt{25³}$$ = $$\sqrt{(5²)³}$$ = $$\sqrt{(5³)²}$$ = |5³| = 5³ = 125
д) $$\sqrt{8 ⋅ 162}$$ = $$\sqrt{8 ⋅ 2 ⋅ 81}$$ = $$\sqrt{16 ⋅ 81}$$ = $$\sqrt{16}$$ ⋅ $$\sqrt{81}$$ = 4 ⋅ 9 = 36
е) $$\sqrt{96 ⋅ 486}$$ = $$\sqrt{16 ⋅ 6 ⋅ 6 ⋅ 81}$$ = $$\sqrt{16 ⋅ 36 ⋅ 81}$$ = $$\sqrt{16}$$ ⋅ $$\sqrt{36}$$ ⋅ $$\sqrt{81}$$ = 4 ⋅ 6 ⋅ 9 = 216
ж) $$\sqrt{750 ⋅ 270}$$ = $$\sqrt{25 ⋅ 3 ⋅ 10 ⋅ 9 ⋅ 3 ⋅ 10}$$ = $$\sqrt{25 ⋅ 100 ⋅ 81}$$ = $$\sqrt{25}$$ ⋅ $$\sqrt{100}$$ ⋅ $$\sqrt{81}$$ = 5 ⋅ 10 ⋅ 9 = 450
з) $$\sqrt{194 ⋅ 776}$$ = $$\sqrt{97 ⋅ 2 ⋅ 97 ⋅ 8}$$ = $$\sqrt{16 ⋅ 97²}$$ = $$\sqrt{16}$$ ⋅ $$\sqrt{97²}$$ = 4 ⋅ 97 = 388