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2c470a49
Найдите значение выражения
7
⋅
14
⋅
8
\sqrt{7}\cdot \sqrt{14}\cdot \sqrt{8}
7
⋅
14
⋅
8
Ответ:
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Решение
7
⋅
14
⋅
8
=
7
⋅
2
⋅
7
⋅
2
3
=
7
⋅
2
⋅
7
⋅
2
⋅
2
=
2
⋅
(
2
⋅
2
)
⋅
(
7
⋅
7
)
=
2
⋅
2
⋅
7
=
28
\begin{aligned}
{}& \sqrt{7}\cdot \sqrt{14}\cdot \sqrt{8} = \sqrt{7}\cdot \sqrt{2\cdot 7}\cdot \sqrt{2^{3}} = \\
& \sqrt{7}\cdot \sqrt{2}\cdot \sqrt{7}\cdot 2\cdot \sqrt{2} = \\
& 2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 2\cdot 2\cdot 7 = 28
\end{aligned}
7
⋅
14
⋅
8
=
7
⋅
2
⋅
7
⋅
2
3
=
7
⋅
2
⋅
7
⋅
2
⋅
2
=
2
⋅
(
2
⋅
2
)
⋅
(
7
⋅
7
)
=
2
⋅
2
⋅
7
=
28
Ответ:
28
28
28
.
