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Найдите значение выражения
2
3
⋅
6
11
⋅
33
2\sqrt{3}\cdot 6\sqrt{11}\cdot \sqrt{33}
2
3
⋅
6
11
⋅
33
Ответ:
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Решение
2
3
⋅
6
11
⋅
33
=
2
⋅
3
⋅
6
⋅
11
⋅
3
⋅
11
=
2
⋅
6
⋅
3
⋅
11
⋅
3
⋅
11
=
12
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
12
⋅
3
⋅
11
=
396
\begin{aligned}
{}& 2\sqrt{3}\cdot 6\sqrt{11}\cdot \sqrt{33} = 2\cdot \sqrt{3}\cdot 6\cdot \sqrt{11}\cdot \sqrt{3\cdot 11} = \\
& 2\cdot 6\cdot \sqrt{3}\cdot \sqrt{11}\cdot \sqrt{3}\cdot \sqrt{11} = \\
& 12\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 12\cdot 3\cdot 11 = 396
\end{aligned}
2
3
⋅
6
11
⋅
33
=
2
⋅
3
⋅
6
⋅
11
⋅
3
⋅
11
=
2
⋅
6
⋅
3
⋅
11
⋅
3
⋅
11
=
12
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
12
⋅
3
⋅
11
=
396
Ответ:
396
396
396
.
