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Найдите значение выражения
11
⋅
22
⋅
50
\sqrt{11}\cdot \sqrt{22}\cdot \sqrt{50}
11
⋅
22
⋅
50
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Решение
11
⋅
22
⋅
50
=
11
⋅
2
⋅
11
⋅
2
⋅
25
=
11
⋅
2
⋅
11
⋅
5
⋅
2
=
5
⋅
(
2
⋅
2
)
⋅
(
11
⋅
11
)
=
5
⋅
2
⋅
11
=
110
\begin{aligned}
{}& \sqrt{11}\cdot \sqrt{22}\cdot \sqrt{50} = \sqrt{11}\cdot \sqrt{2\cdot 11}\cdot \sqrt{2\cdot 25} = \\
& \sqrt{11}\cdot \sqrt{2}\cdot \sqrt{11}\cdot 5\cdot \sqrt{2} = \\
& 5\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 5\cdot 2\cdot 11 = 110
\end{aligned}
11
⋅
22
⋅
50
=
11
⋅
2
⋅
11
⋅
2
⋅
25
=
11
⋅
2
⋅
11
⋅
5
⋅
2
=
5
⋅
(
2
⋅
2
)
⋅
(
11
⋅
11
)
=
5
⋅
2
⋅
11
=
110
Ответ:
110
110
110
.
