Школьник
Студент
Учитель
Личный кабинет
Назад
Вычисления
Банк ОГЭ
Скопировать ссылку
415ec1c8
Найдите значение выражения
30
⋅
60
⋅
2
\sqrt{30}\cdot \sqrt{60}\cdot \sqrt{2}
30
⋅
60
⋅
2
Ответ:
Ответить
Показать ответ
Ответ
Скрыть решение
Решение
Сообщить об ошибке
Решение
30
⋅
60
⋅
2
=
2
⋅
3
⋅
5
⋅
4
⋅
3
⋅
5
⋅
2
=
2
⋅
3
⋅
5
⋅
2
⋅
3
⋅
5
⋅
2
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
5
⋅
5
)
=
2
⋅
2
⋅
3
⋅
5
=
60
\begin{aligned}
{}& \sqrt{30}\cdot \sqrt{60}\cdot \sqrt{2} = \sqrt{2\cdot 3\cdot 5}\cdot \sqrt{4\cdot 3\cdot 5}\cdot \sqrt{2} = \\
& \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{5}\cdot 2\cdot \sqrt{3}\cdot \sqrt{5}\cdot \sqrt{2} = \\
& 2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{5}\cdot\sqrt{5}) = \\
& 2\cdot 2\cdot 3\cdot 5 = 60
\end{aligned}
30
⋅
60
⋅
2
=
2
⋅
3
⋅
5
⋅
4
⋅
3
⋅
5
⋅
2
=
2
⋅
3
⋅
5
⋅
2
⋅
3
⋅
5
⋅
2
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
5
⋅
5
)
=
2
⋅
2
⋅
3
⋅
5
=
60
Ответ:
60
60
60
.
