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Найдите значение выражения
50
⋅
94
47
\dfrac{\sqrt{50}\cdot \sqrt{94}}{\sqrt{47}}
47
50
⋅
94
Ответ:
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Решение
50
⋅
94
47
=
2
⋅
25
⋅
2
⋅
47
47
=
5
⋅
2
⋅
2
⋅
47
47
=
5
⋅
(
2
⋅
2
)
⋅
47
47
=
5
⋅
2
⋅
47
47
=
10
\begin{aligned}
{}& \dfrac{\sqrt{50}\cdot \sqrt{94}}{\sqrt{47}} = \dfrac{\sqrt{2\cdot 25}\cdot\sqrt{2\cdot 47}}{\sqrt{47}} = \\
& \dfrac{5\cdot \sqrt{2}\cdot \sqrt{2}\cdot \sqrt{47}}{\sqrt{47}} = \\
& \dfrac{5\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{47}}{\sqrt{47}} = \\
& \dfrac{5\cdot 2\cdot \sqrt{47}}{\sqrt{47}} = 10
\end{aligned}
47
50
⋅
94
=
47
2
⋅
25
⋅
2
⋅
47
=
47
5
⋅
2
⋅
2
⋅
47
=
47
5
⋅
(
2
⋅
2
)
⋅
47
=
47
5
⋅
2
⋅
47
=
10
Ответ:
10
10
10
.
