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Найдите значение выражения
8
⋅
27
⋅
6
\sqrt{8}\cdot \sqrt{27}\cdot \sqrt{6}
8
⋅
27
⋅
6
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Решение
8
⋅
27
⋅
6
=
2
3
⋅
3
3
⋅
2
⋅
3
=
2
⋅
2
⋅
3
⋅
3
⋅
2
⋅
3
=
6
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
6
⋅
2
⋅
3
=
36
\begin{aligned}
{}& \sqrt{8}\cdot \sqrt{27}\cdot \sqrt{6} = \sqrt{2^{3}}\cdot \sqrt{3^{3}}\cdot \sqrt{2\cdot 3} = \\
& 2\cdot \sqrt{2}\cdot 3\cdot \sqrt{3}\cdot \sqrt{2}\cdot \sqrt{3} = \\
& 6\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 6\cdot 2\cdot 3 = 36
\end{aligned}
8
⋅
27
⋅
6
=
2
3
⋅
3
3
⋅
2
⋅
3
=
2
⋅
2
⋅
3
⋅
3
⋅
2
⋅
3
=
6
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
6
⋅
2
⋅
3
=
36
Ответ:
36
36
36
.
