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Найдите значение выражения
7
⋅
8
⋅
56
\sqrt{7}\cdot \sqrt{8}\cdot \sqrt{56}
7
⋅
8
⋅
56
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Решение
7
⋅
8
⋅
56
=
7
⋅
2
3
⋅
8
⋅
7
=
7
⋅
2
⋅
2
⋅
2
⋅
2
⋅
7
=
4
⋅
(
2
⋅
2
)
⋅
(
7
⋅
7
)
=
4
⋅
2
⋅
7
=
56
\begin{aligned}
{}& \sqrt{7}\cdot \sqrt{8}\cdot \sqrt{56} = \sqrt{7}\cdot \sqrt{2^{3}}\cdot \sqrt{8\cdot 7} = \\
& \sqrt{7}\cdot 2\cdot \sqrt{2}\cdot 2\cdot \sqrt{2}\cdot \sqrt{7} = \\
& 4\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 4\cdot 2\cdot 7 = 56
\end{aligned}
7
⋅
8
⋅
56
=
7
⋅
2
3
⋅
8
⋅
7
=
7
⋅
2
⋅
2
⋅
2
⋅
2
⋅
7
=
4
⋅
(
2
⋅
2
)
⋅
(
7
⋅
7
)
=
4
⋅
2
⋅
7
=
56
Ответ:
56
56
56
.
