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Найдите значение выражения
8
⋅
175
56
\dfrac{\sqrt{8}\cdot \sqrt{175}}{\sqrt{56}}
56
8
⋅
175
Ответ:
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Решение
8
⋅
175
56
=
2
3
⋅
25
⋅
7
8
⋅
7
=
2
⋅
2
⋅
5
⋅
7
2
⋅
2
⋅
7
=
10
⋅
2
⋅
7
2
⋅
2
⋅
7
=
5
\begin{aligned}
{}& \dfrac{\sqrt{8}\cdot \sqrt{175}}{\sqrt{56}} = \dfrac{\sqrt{2^{3}}\cdot\sqrt{25\cdot 7}}{\sqrt{8\cdot 7}} = \\
& \dfrac{2\cdot \sqrt{2}\cdot 5\cdot \sqrt{7}}{2\cdot \sqrt{2}\cdot \sqrt{7}} = \\
& \dfrac{10\cdot \sqrt{2}\cdot \sqrt{7}}{2\cdot \sqrt{2}\cdot \sqrt{7}} = \\
& 5
\end{aligned}
56
8
⋅
175
=
8
⋅
7
2
3
⋅
25
⋅
7
=
2
⋅
2
⋅
7
2
⋅
2
⋅
5
⋅
7
=
2
⋅
2
⋅
7
10
⋅
2
⋅
7
=
5
Ответ:
5
5
5
.
