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Найдите значение выражения
2
5
⋅
2
7
⋅
35
2\sqrt{5}\cdot 2\sqrt{7}\cdot \sqrt{35}
2
5
⋅
2
7
⋅
35
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Решение
2
5
⋅
2
7
⋅
35
=
2
⋅
5
⋅
2
⋅
7
⋅
5
⋅
7
=
2
⋅
2
⋅
5
⋅
7
⋅
5
⋅
7
=
4
⋅
(
5
⋅
5
)
⋅
(
7
⋅
7
)
=
4
⋅
5
⋅
7
=
140
\begin{aligned}
{}& 2\sqrt{5}\cdot 2\sqrt{7}\cdot \sqrt{35} = 2\cdot \sqrt{5}\cdot 2\cdot \sqrt{7}\cdot \sqrt{5\cdot 7} = \\
& 2\cdot 2\cdot \sqrt{5}\cdot \sqrt{7}\cdot \sqrt{5}\cdot \sqrt{7} = \\
& 4\cdot (\sqrt{5}\cdot\sqrt{5})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 4\cdot 5\cdot 7 = 140
\end{aligned}
2
5
⋅
2
7
⋅
35
=
2
⋅
5
⋅
2
⋅
7
⋅
5
⋅
7
=
2
⋅
2
⋅
5
⋅
7
⋅
5
⋅
7
=
4
⋅
(
5
⋅
5
)
⋅
(
7
⋅
7
)
=
4
⋅
5
⋅
7
=
140
Ответ:
140
140
140
.
