Найдите значение выражения √36x4 / y2 при x = 6 и y = 9.
Источник: Ященко ОГЭ 2025 (36 вар.)
Решение:
√36x4 / y2 = √6 ⋅ 6 ⋅ x2⋅2 / y2 = √ 62 ⋅ (x2 )2 / y2 = √(6 ⋅ x2 )2 / y2 = √(6 ⋅ x2 /y)2 = 6 ⋅ x2 / y
6 ⋅ x2 / y = 6 ⋅ 62 / 9 = 6 ⋅ 6 ⋅ 6 / 3 ⋅ 3 = 2 ⋅ 2 ⋅ 6 / 1 = 24
Ответ: 24