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Найдите значение выражения
50
⋅
90
20
\dfrac{\sqrt{50}\cdot \sqrt{90}}{\sqrt{20}}
20
50
⋅
90
Ответ:
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Решение
50
⋅
90
20
=
2
⋅
25
⋅
2
⋅
9
⋅
5
4
⋅
5
=
5
⋅
2
⋅
3
⋅
2
⋅
5
2
⋅
5
=
15
⋅
(
2
⋅
2
)
⋅
5
2
⋅
5
=
15
⋅
2
⋅
5
2
⋅
5
=
15
\begin{aligned}
{}& \dfrac{\sqrt{50}\cdot \sqrt{90}}{\sqrt{20}} = \dfrac{\sqrt{2\cdot 25}\cdot\sqrt{2\cdot 9\cdot 5}}{\sqrt{4\cdot 5}} = \\
& \dfrac{5\cdot \sqrt{2}\cdot 3\cdot \sqrt{2}\cdot \sqrt{5}}{2\cdot \sqrt{5}} = \\
& \dfrac{15\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{5}}{2\cdot \sqrt{5}} = \\
& \dfrac{15\cdot 2\cdot \sqrt{5}}{2\cdot \sqrt{5}} = 15
\end{aligned}
20
50
⋅
90
=
4
⋅
5
2
⋅
25
⋅
2
⋅
9
⋅
5
=
2
⋅
5
5
⋅
2
⋅
3
⋅
2
⋅
5
=
2
⋅
5
15
⋅
(
2
⋅
2
)
⋅
5
=
2
⋅
5
15
⋅
2
⋅
5
=
15
Ответ:
15
15
15
.
