Школьник
Студент
Учитель
Личный кабинет
Назад
Вычисления
Банк ОГЭ
Скопировать ссылку
d80693ad
Найдите значение выражения
21
⋅
42
⋅
8
\sqrt{21}\cdot \sqrt{42}\cdot \sqrt{8}
21
⋅
42
⋅
8
Ответ:
Ответить
Показать ответ
Ответ
Показать решение
Решение
Сообщить об ошибке
Решение
21
⋅
42
⋅
8
=
3
⋅
7
⋅
2
⋅
3
⋅
7
⋅
2
3
=
3
⋅
7
⋅
2
⋅
3
⋅
7
⋅
2
⋅
2
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
7
⋅
7
)
=
2
⋅
2
⋅
3
⋅
7
=
84
\begin{aligned}
{}& \sqrt{21}\cdot \sqrt{42}\cdot \sqrt{8} = \sqrt{3\cdot 7}\cdot \sqrt{2\cdot 3\cdot 7}\cdot \sqrt{2^{3}} = \\
& \sqrt{3}\cdot \sqrt{7}\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{7}\cdot 2\cdot \sqrt{2} = \\
& 2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 2\cdot 2\cdot 3\cdot 7 = 84
\end{aligned}
21
⋅
42
⋅
8
=
3
⋅
7
⋅
2
⋅
3
⋅
7
⋅
2
3
=
3
⋅
7
⋅
2
⋅
3
⋅
7
⋅
2
⋅
2
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
7
⋅
7
)
=
2
⋅
2
⋅
3
⋅
7
=
84
Ответ:
84
84
84
.
