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Найдите значение выражения
12
⋅
22
⋅
66
\sqrt{12}\cdot \sqrt{22}\cdot \sqrt{66}
12
⋅
22
⋅
66
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Решение
12
⋅
22
⋅
66
=
4
⋅
3
⋅
2
⋅
11
⋅
2
⋅
3
⋅
11
=
2
⋅
3
⋅
2
⋅
11
⋅
2
⋅
3
⋅
11
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
2
⋅
2
⋅
3
⋅
11
=
132
\begin{aligned}
{}& \sqrt{12}\cdot \sqrt{22}\cdot \sqrt{66} = \sqrt{4\cdot 3}\cdot \sqrt{2\cdot 11}\cdot \sqrt{2\cdot 3\cdot 11} = \\
& 2\cdot \sqrt{3}\cdot \sqrt{2}\cdot \sqrt{11}\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{11} = \\
& 2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 2\cdot 2\cdot 3\cdot 11 = 132
\end{aligned}
12
⋅
22
⋅
66
=
4
⋅
3
⋅
2
⋅
11
⋅
2
⋅
3
⋅
11
=
2
⋅
3
⋅
2
⋅
11
⋅
2
⋅
3
⋅
11
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
2
⋅
2
⋅
3
⋅
11
=
132
Ответ:
132
132
132
.
