Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 397

а) разложим на простые множители
2304 | 2 1152 | 2 576 | 2 288 | 2 144 | 2 72 | 2 36 | 2 18 | 2 9 | 3 3 | 3 1
$$\sqrt{2304}$$ = $$\sqrt{2⁸ ⋅ 3²}$$ = $$\sqrt{2⁸}$$ ⋅ $$\sqrt{3²}$$ = $$\sqrt{(2⁴)²}$$ ⋅ $$\sqrt{3²}$$ = |2⁴| ⋅ |3| = |16| ⋅ |3| = 16 ⋅ 3 = 48
б) разложим на простые множители
18225 | 3 6075 | 3 2025 | 3 675 | 3 225 | 3 75 | 3 25 | 5 5 | 5 1
$$\sqrt{18225}$$ = $$\sqrt{3⁶ ⋅ 5²}$$ = $$\sqrt{3⁶}$$ ⋅ $$\sqrt{5²}$$ = $$\sqrt{(3³)²}$$ ⋅ $$\sqrt{5²}$$ = |3³| ⋅ |5| = |27| ⋅ |5| = 27 ⋅ 5 = 135
в) разложим на простые множители
254016 | 2 127008 | 2 63504 | 2 31752 | 2 15876 | 2 7938 | 2 3969 | 3 1323 | 3 441 | 3 147 | 3 49 | 7 7 | 7 1
$$\sqrt{254016}$$ = $$\sqrt{2⁶ ⋅ 3⁴ ⋅ 7²}$$ = $$\sqrt{2⁶}$$ ⋅ $$\sqrt{3⁴}$$ ⋅ $$\sqrt{7²}$$ = $$\sqrt{(2³)²}$$ ⋅ $$\sqrt{(3²)²}$$ ⋅ $$\sqrt{7²}$$ = |2³| ⋅ |3²| ⋅ |7| = |8| ⋅ |9| ⋅ |7| = 8 ⋅ 9 ⋅ 7 = 504