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5170593a
Найдите значение выражения
2
⋅
3
⋅
24
\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{24}
2
⋅
3
⋅
24
Ответ:
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Решение
2
⋅
3
⋅
24
=
2
⋅
3
⋅
8
⋅
3
=
2
⋅
3
⋅
2
⋅
2
⋅
3
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
2
⋅
2
⋅
3
=
12
\begin{aligned}
{}& \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{24} = \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{8\cdot 3} = \\
& \sqrt{2}\cdot \sqrt{3}\cdot 2\cdot \sqrt{2}\cdot \sqrt{3} = \\
& 2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 2\cdot 2\cdot 3 = 12
\end{aligned}
2
⋅
3
⋅
24
=
2
⋅
3
⋅
8
⋅
3
=
2
⋅
3
⋅
2
⋅
2
⋅
3
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
2
⋅
2
⋅
3
=
12
Ответ:
12
12
12
.
