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Найдите значение выражения
2
⋅
63
⋅
56
\sqrt{2}\cdot \sqrt{63}\cdot \sqrt{56}
2
⋅
63
⋅
56
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Решение
2
⋅
63
⋅
56
=
2
⋅
9
⋅
7
⋅
8
⋅
7
=
2
⋅
3
⋅
7
⋅
2
⋅
2
⋅
7
=
6
⋅
(
2
⋅
2
)
⋅
(
7
⋅
7
)
=
6
⋅
2
⋅
7
=
84
\begin{aligned}
{}& \sqrt{2}\cdot \sqrt{63}\cdot \sqrt{56} = \sqrt{2}\cdot \sqrt{9\cdot 7}\cdot \sqrt{8\cdot 7} = \\
& \sqrt{2}\cdot 3\cdot \sqrt{7}\cdot 2\cdot \sqrt{2}\cdot \sqrt{7} = \\
& 6\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 6\cdot 2\cdot 7 = 84
\end{aligned}
2
⋅
63
⋅
56
=
2
⋅
9
⋅
7
⋅
8
⋅
7
=
2
⋅
3
⋅
7
⋅
2
⋅
2
⋅
7
=
6
⋅
(
2
⋅
2
)
⋅
(
7
⋅
7
)
=
6
⋅
2
⋅
7
=
84
Ответ:
84
84
84
.
