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Найдите значение выражения
6
⋅
72
⋅
12
\sqrt{6}\cdot \sqrt{72}\cdot \sqrt{12}
6
⋅
72
⋅
12
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Решение
6
⋅
72
⋅
12
=
2
⋅
3
⋅
8
⋅
9
⋅
4
⋅
3
=
2
⋅
3
⋅
6
⋅
2
⋅
2
⋅
3
=
12
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
12
⋅
2
⋅
3
=
72
\begin{aligned}
{}& \sqrt{6}\cdot \sqrt{72}\cdot \sqrt{12} = \sqrt{2\cdot 3}\cdot \sqrt{8\cdot 9}\cdot \sqrt{4\cdot 3} = \\
& \sqrt{2}\cdot \sqrt{3}\cdot 6\cdot \sqrt{2}\cdot 2\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
⋅
72
⋅
12
=
2
⋅
3
⋅
8
⋅
9
⋅
4
⋅
3
=
2
⋅
3
⋅
6
⋅
2
⋅
2
⋅
3
=
12
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
12
⋅
2
⋅
3
=
72
Ответ:
72
72
72
.
