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Найдите значение выражения
11
⋅
12
⋅
33
\sqrt{11}\cdot \sqrt{12}\cdot \sqrt{33}
11
⋅
12
⋅
33
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Решение
11
⋅
12
⋅
33
=
11
⋅
4
⋅
3
⋅
3
⋅
11
=
11
⋅
2
⋅
3
⋅
3
⋅
11
=
2
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
2
⋅
3
⋅
11
=
66
\begin{aligned}
{}& \sqrt{11}\cdot \sqrt{12}\cdot \sqrt{33} = \sqrt{11}\cdot \sqrt{4\cdot 3}\cdot \sqrt{3\cdot 11} = \\
& \sqrt{11}\cdot 2\cdot \sqrt{3}\cdot \sqrt{3}\cdot \sqrt{11} = \\
& 2\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 2\cdot 3\cdot 11 = 66
\end{aligned}
11
⋅
12
⋅
33
=
11
⋅
4
⋅
3
⋅
3
⋅
11
=
11
⋅
2
⋅
3
⋅
3
⋅
11
=
2
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
2
⋅
3
⋅
11
=
66
Ответ:
66
66
66
.
