Школьник
Студент
Учитель
Личный кабинет
Назад
Вычисления
Банк ОГЭ
Скопировать ссылку
34946c7e
Найдите значение выражения
40
⋅
110
11
\dfrac{\sqrt{40}\cdot \sqrt{110}}{\sqrt{11}}
11
40
⋅
110
Ответ:
Ответить
Показать ответ
Ответ
Скрыть решение
Решение
Сообщить об ошибке
Решение
40
⋅
110
11
=
8
⋅
5
⋅
2
⋅
5
⋅
11
11
=
2
⋅
2
⋅
5
⋅
2
⋅
5
⋅
11
11
=
2
⋅
(
2
⋅
2
)
⋅
(
5
⋅
5
)
⋅
11
11
=
2
⋅
2
⋅
5
⋅
11
11
=
20
\begin{aligned}
{}& \dfrac{\sqrt{40}\cdot \sqrt{110}}{\sqrt{11}} = \dfrac{\sqrt{8\cdot 5}\cdot\sqrt{2\cdot 5\cdot 11}}{\sqrt{11}} = \\
& \dfrac{2\cdot \sqrt{2}\cdot \sqrt{5}\cdot \sqrt{2}\cdot \sqrt{5}\cdot \sqrt{11}}{\sqrt{11}} = \\
& \dfrac{2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{5}\cdot\sqrt{5})\cdot \sqrt{11}}{\sqrt{11}} = \\
& \dfrac{2\cdot 2\cdot 5\cdot \sqrt{11}}{\sqrt{11}} = 20
\end{aligned}
11
40
⋅
110
=
11
8
⋅
5
⋅
2
⋅
5
⋅
11
=
11
2
⋅
2
⋅
5
⋅
2
⋅
5
⋅
11
=
11
2
⋅
(
2
⋅
2
)
⋅
(
5
⋅
5
)
⋅
11
=
11
2
⋅
2
⋅
5
⋅
11
=
20
Ответ:
20
20
20
.
