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Найдите значение выражения
6
⋅
32
⋅
27
\sqrt{6}\cdot \sqrt{32}\cdot \sqrt{27}
6
⋅
32
⋅
27
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Решение
6
⋅
32
⋅
27
=
2
⋅
3
⋅
2
5
⋅
3
3
=
2
⋅
3
⋅
4
⋅
2
⋅
3
⋅
3
=
12
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
12
⋅
2
⋅
3
=
72
\begin{aligned}
{}& \sqrt{6}\cdot \sqrt{32}\cdot \sqrt{27} = \sqrt{2\cdot 3}\cdot \sqrt{2^{5}}\cdot \sqrt{3^{3}} = \\
& \sqrt{2}\cdot \sqrt{3}\cdot 4\cdot \sqrt{2}\cdot 3\cdot \sqrt{3} = \\
& 12\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 12\cdot 2\cdot 3 = 72
\end{aligned}
6
⋅
32
⋅
27
=
2
⋅
3
⋅
2
5
⋅
3
3
=
2
⋅
3
⋅
4
⋅
2
⋅
3
⋅
3
=
12
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
12
⋅
2
⋅
3
=
72
Ответ:
72
72
72
.
