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4f03c142
Найдите значение выражения
8
⋅
24
⋅
12
\sqrt{8}\cdot \sqrt{24}\cdot \sqrt{12}
8
⋅
24
⋅
12
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Решение
8
⋅
24
⋅
12
=
2
3
⋅
8
⋅
3
⋅
4
⋅
3
=
2
⋅
2
⋅
2
⋅
2
⋅
3
⋅
2
⋅
3
=
8
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
8
⋅
2
⋅
3
=
48
\begin{aligned}
{}& \sqrt{8}\cdot \sqrt{24}\cdot \sqrt{12} = \sqrt{2^{3}}\cdot \sqrt{8\cdot 3}\cdot \sqrt{4\cdot 3} = \\
& 2\cdot \sqrt{2}\cdot 2\cdot \sqrt{2}\cdot \sqrt{3}\cdot 2\cdot \sqrt{3} = \\
& 8\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 8\cdot 2\cdot 3 = 48
\end{aligned}
8
⋅
24
⋅
12
=
2
3
⋅
8
⋅
3
⋅
4
⋅
3
=
2
⋅
2
⋅
2
⋅
2
⋅
3
⋅
2
⋅
3
=
8
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
8
⋅
2
⋅
3
=
48
Ответ:
48
48
48
.
