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Найдите значение выражения
32
⋅
54
⋅
12
\sqrt{32}\cdot \sqrt{54}\cdot \sqrt{12}
32
⋅
54
⋅
12
Ответ:
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Решение
32
⋅
54
⋅
12
=
2
5
⋅
2
⋅
27
⋅
4
⋅
3
=
4
⋅
2
⋅
3
⋅
2
⋅
3
⋅
2
⋅
3
=
24
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
24
⋅
2
⋅
3
=
144
\begin{aligned}
{}& \sqrt{32}\cdot \sqrt{54}\cdot \sqrt{12} = \sqrt{2^{5}}\cdot \sqrt{2\cdot 27}\cdot \sqrt{4\cdot 3} = \\
& 4\cdot \sqrt{2}\cdot 3\cdot \sqrt{2}\cdot \sqrt{3}\cdot 2\cdot \sqrt{3} = \\
& 24\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 24\cdot 2\cdot 3 = 144
\end{aligned}
32
⋅
54
⋅
12
=
2
5
⋅
2
⋅
27
⋅
4
⋅
3
=
4
⋅
2
⋅
3
⋅
2
⋅
3
⋅
2
⋅
3
=
24
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
24
⋅
2
⋅
3
=
144
Ответ:
144
144
144
.
