Школьник
Студент
Учитель
Личный кабинет
Назад
Вычисления
Банк ОГЭ
Скопировать ссылку
4c4251ab
Найдите значение выражения
3
⋅
54
⋅
8
\sqrt{3}\cdot \sqrt{54}\cdot \sqrt{8}
3
⋅
54
⋅
8
Ответ:
Ответить
Показать ответ
Ответ
Скрыть решение
Решение
Сообщить об ошибке
Решение
3
⋅
54
⋅
8
=
3
⋅
2
⋅
27
⋅
2
3
=
3
⋅
3
⋅
2
⋅
3
⋅
2
⋅
2
=
6
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
6
⋅
2
⋅
3
=
36
\begin{aligned}
{}& \sqrt{3}\cdot \sqrt{54}\cdot \sqrt{8} = \sqrt{3}\cdot \sqrt{2\cdot 27}\cdot \sqrt{2^{3}} = \\
& \sqrt{3}\cdot 3\cdot \sqrt{2}\cdot \sqrt{3}\cdot 2\cdot \sqrt{2} = \\
& 6\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 6\cdot 2\cdot 3 = 36
\end{aligned}
3
⋅
54
⋅
8
=
3
⋅
2
⋅
27
⋅
2
3
=
3
⋅
3
⋅
2
⋅
3
⋅
2
⋅
2
=
6
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
6
⋅
2
⋅
3
=
36
Ответ:
36
36
36
.
