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Найдите значение выражения
3
2
⋅
4
11
⋅
22
3\sqrt{2}\cdot 4\sqrt{11}\cdot \sqrt{22}
3
2
⋅
4
11
⋅
22
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Решение
3
2
⋅
4
11
⋅
22
=
3
⋅
2
⋅
4
⋅
11
⋅
2
⋅
11
=
3
⋅
4
⋅
2
⋅
11
⋅
2
⋅
11
=
12
⋅
(
2
⋅
2
)
⋅
(
11
⋅
11
)
=
12
⋅
2
⋅
11
=
264
\begin{aligned}
{}& 3\sqrt{2}\cdot 4\sqrt{11}\cdot \sqrt{22} = 3\cdot \sqrt{2}\cdot 4\cdot \sqrt{11}\cdot \sqrt{2\cdot 11} = \\
& 3\cdot 4\cdot \sqrt{2}\cdot \sqrt{11}\cdot \sqrt{2}\cdot \sqrt{11} = \\
& 12\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 12\cdot 2\cdot 11 = 264
\end{aligned}
3
2
⋅
4
11
⋅
22
=
3
⋅
2
⋅
4
⋅
11
⋅
2
⋅
11
=
3
⋅
4
⋅
2
⋅
11
⋅
2
⋅
11
=
12
⋅
(
2
⋅
2
)
⋅
(
11
⋅
11
)
=
12
⋅
2
⋅
11
=
264
Ответ:
264
264
264
.
