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Найдите значение выражения
2
3
⋅
5
11
⋅
33
2\sqrt{3}\cdot 5\sqrt{11}\cdot \sqrt{33}
2
3
⋅
5
11
⋅
33
Ответ:
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Решение
2
3
⋅
5
11
⋅
33
=
2
⋅
3
⋅
5
⋅
11
⋅
3
⋅
11
=
2
⋅
5
⋅
3
⋅
11
⋅
3
⋅
11
=
10
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
10
⋅
3
⋅
11
=
330
\begin{aligned}
{}& 2\sqrt{3}\cdot 5\sqrt{11}\cdot \sqrt{33} = 2\cdot \sqrt{3}\cdot 5\cdot \sqrt{11}\cdot \sqrt{3\cdot 11} = \\
& 2\cdot 5\cdot \sqrt{3}\cdot \sqrt{11}\cdot \sqrt{3}\cdot \sqrt{11} = \\
& 10\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 10\cdot 3\cdot 11 = 330
\end{aligned}
2
3
⋅
5
11
⋅
33
=
2
⋅
3
⋅
5
⋅
11
⋅
3
⋅
11
=
2
⋅
5
⋅
3
⋅
11
⋅
3
⋅
11
=
10
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
10
⋅
3
⋅
11
=
330
Ответ:
330
330
330
.
