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Найдите значение выражения
14
⋅
32
⋅
28
\sqrt{14}\cdot \sqrt{32}\cdot \sqrt{28}
14
⋅
32
⋅
28
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Решение
14
⋅
32
⋅
28
=
2
⋅
7
⋅
2
5
⋅
4
⋅
7
=
2
⋅
7
⋅
4
⋅
2
⋅
2
⋅
7
=
8
⋅
(
2
⋅
2
)
⋅
(
7
⋅
7
)
=
8
⋅
2
⋅
7
=
112
\begin{aligned}
{}& \sqrt{14}\cdot \sqrt{32}\cdot \sqrt{28} = \sqrt{2\cdot 7}\cdot \sqrt{2^{5}}\cdot \sqrt{4\cdot 7} = \\
& \sqrt{2}\cdot \sqrt{7}\cdot 4\cdot \sqrt{2}\cdot 2\cdot \sqrt{7} = \\
& 8\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 8\cdot 2\cdot 7 = 112
\end{aligned}
14
⋅
32
⋅
28
=
2
⋅
7
⋅
2
5
⋅
4
⋅
7
=
2
⋅
7
⋅
4
⋅
2
⋅
2
⋅
7
=
8
⋅
(
2
⋅
2
)
⋅
(
7
⋅
7
)
=
8
⋅
2
⋅
7
=
112
Ответ:
112
112
112
.
