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Найдите значение выражения
8
⋅
48
⋅
24
\sqrt{8}\cdot \sqrt{48}\cdot \sqrt{24}
8
⋅
48
⋅
24
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Решение
8
⋅
48
⋅
24
=
2
3
⋅
16
⋅
3
⋅
8
⋅
3
=
2
⋅
2
⋅
4
⋅
3
⋅
2
⋅
2
⋅
3
=
16
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
16
⋅
2
⋅
3
=
96
\begin{aligned}
{}& \sqrt{8}\cdot \sqrt{48}\cdot \sqrt{24} = \sqrt{2^{3}}\cdot \sqrt{16\cdot 3}\cdot \sqrt{8\cdot 3} = \\
& 2\cdot \sqrt{2}\cdot 4\cdot \sqrt{3}\cdot 2\cdot \sqrt{2}\cdot \sqrt{3} = \\
& 16\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 16\cdot 2\cdot 3 = 96
\end{aligned}
8
⋅
48
⋅
24
=
2
3
⋅
16
⋅
3
⋅
8
⋅
3
=
2
⋅
2
⋅
4
⋅
3
⋅
2
⋅
2
⋅
3
=
16
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
16
⋅
2
⋅
3
=
96
Ответ:
96
96
96
.
