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Найдите значение выражения
5
3
⋅
3
11
⋅
33
5\sqrt{3}\cdot 3\sqrt{11}\cdot \sqrt{33}
5
3
⋅
3
11
⋅
33
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Решение
5
3
⋅
3
11
⋅
33
=
5
⋅
3
⋅
3
⋅
11
⋅
3
⋅
11
=
5
⋅
3
⋅
3
⋅
11
⋅
3
⋅
11
=
15
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
15
⋅
3
⋅
11
=
495
\begin{aligned}
{}& 5\sqrt{3}\cdot 3\sqrt{11}\cdot \sqrt{33} = 5\cdot \sqrt{3}\cdot 3\cdot \sqrt{11}\cdot \sqrt{3\cdot 11} = \\
& 5\cdot 3\cdot \sqrt{3}\cdot \sqrt{11}\cdot \sqrt{3}\cdot \sqrt{11} = \\
& 15\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 15\cdot 3\cdot 11 = 495
\end{aligned}
5
3
⋅
3
11
⋅
33
=
5
⋅
3
⋅
3
⋅
11
⋅
3
⋅
11
=
5
⋅
3
⋅
3
⋅
11
⋅
3
⋅
11
=
15
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
15
⋅
3
⋅
11
=
495
Ответ:
495
495
495
.
