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676f9549
Найдите значение выражения
5
5
⋅
3
7
⋅
35
5\sqrt{5}\cdot 3\sqrt{7}\cdot \sqrt{35}
5
5
⋅
3
7
⋅
35
Ответ:
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Решение
5
5
⋅
3
7
⋅
35
=
5
⋅
5
⋅
3
⋅
7
⋅
5
⋅
7
=
5
⋅
3
⋅
5
⋅
7
⋅
5
⋅
7
=
15
⋅
(
5
⋅
5
)
⋅
(
7
⋅
7
)
=
15
⋅
5
⋅
7
=
525
\begin{aligned}
{}& 5\sqrt{5}\cdot 3\sqrt{7}\cdot \sqrt{35} = 5\cdot \sqrt{5}\cdot 3\cdot \sqrt{7}\cdot \sqrt{5\cdot 7} = \\
& 5\cdot 3\cdot \sqrt{5}\cdot \sqrt{7}\cdot \sqrt{5}\cdot \sqrt{7} = \\
& 15\cdot (\sqrt{5}\cdot\sqrt{5})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 15\cdot 5\cdot 7 = 525
\end{aligned}
5
5
⋅
3
7
⋅
35
=
5
⋅
5
⋅
3
⋅
7
⋅
5
⋅
7
=
5
⋅
3
⋅
5
⋅
7
⋅
5
⋅
7
=
15
⋅
(
5
⋅
5
)
⋅
(
7
⋅
7
)
=
15
⋅
5
⋅
7
=
525
Ответ:
525
525
525
.
