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Найдите значение выражения
6
⋅
88
⋅
33
\sqrt{6}\cdot \sqrt{88}\cdot \sqrt{33}
6
⋅
88
⋅
33
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Решение
6
⋅
88
⋅
33
=
2
⋅
3
⋅
8
⋅
11
⋅
3
⋅
11
=
2
⋅
3
⋅
2
⋅
2
⋅
11
⋅
3
⋅
11
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
2
⋅
2
⋅
3
⋅
11
=
132
\begin{aligned}
{}& \sqrt{6}\cdot \sqrt{88}\cdot \sqrt{33} = \sqrt{2\cdot 3}\cdot \sqrt{8\cdot 11}\cdot \sqrt{3\cdot 11} = \\
& \sqrt{2}\cdot \sqrt{3}\cdot 2\cdot \sqrt{2}\cdot \sqrt{11}\cdot \sqrt{3}\cdot \sqrt{11} = \\
& 2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 2\cdot 2\cdot 3\cdot 11 = 132
\end{aligned}
6
⋅
88
⋅
33
=
2
⋅
3
⋅
8
⋅
11
⋅
3
⋅
11
=
2
⋅
3
⋅
2
⋅
2
⋅
11
⋅
3
⋅
11
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
2
⋅
2
⋅
3
⋅
11
=
132
Ответ:
132
132
132
.
