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