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Найдите значение выражения
5
2
⋅
3
11
⋅
22
5\sqrt{2}\cdot 3\sqrt{11}\cdot \sqrt{22}
5
2
⋅
3
11
⋅
22
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Решение
5
2
⋅
3
11
⋅
22
=
5
⋅
2
⋅
3
⋅
11
⋅
2
⋅
11
=
5
⋅
3
⋅
2
⋅
11
⋅
2
⋅
11
=
15
⋅
(
2
⋅
2
)
⋅
(
11
⋅
11
)
=
15
⋅
2
⋅
11
=
330
\begin{aligned}
{}& 5\sqrt{2}\cdot 3\sqrt{11}\cdot \sqrt{22} = 5\cdot \sqrt{2}\cdot 3\cdot \sqrt{11}\cdot \sqrt{2\cdot 11} = \\
& 5\cdot 3\cdot \sqrt{2}\cdot \sqrt{11}\cdot \sqrt{2}\cdot \sqrt{11} = \\
& 15\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 15\cdot 2\cdot 11 = 330
\end{aligned}
5
2
⋅
3
11
⋅
22
=
5
⋅
2
⋅
3
⋅
11
⋅
2
⋅
11
=
5
⋅
3
⋅
2
⋅
11
⋅
2
⋅
11
=
15
⋅
(
2
⋅
2
)
⋅
(
11
⋅
11
)
=
15
⋅
2
⋅
11
=
330
Ответ:
330
330
330
.
