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Найдите значение выражения
6
⋅
40
60
\dfrac{\sqrt{6}\cdot \sqrt{40}}{\sqrt{60}}
60
6
⋅
40
Ответ:
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Решение
6
⋅
40
60
=
2
⋅
3
⋅
8
⋅
5
4
⋅
3
⋅
5
=
2
⋅
3
⋅
2
⋅
2
⋅
5
2
⋅
3
⋅
5
=
2
⋅
(
2
⋅
2
)
⋅
3
⋅
5
2
⋅
3
⋅
5
=
2
⋅
2
⋅
3
⋅
5
2
⋅
3
⋅
5
=
2
\begin{aligned}
{}& \dfrac{\sqrt{6}\cdot \sqrt{40}}{\sqrt{60}} = \dfrac{\sqrt{2\cdot 3}\cdot\sqrt{8\cdot 5}}{\sqrt{4\cdot 3\cdot 5}} = \\
& \dfrac{\sqrt{2}\cdot \sqrt{3}\cdot 2\cdot \sqrt{2}\cdot \sqrt{5}}{2\cdot \sqrt{3}\cdot \sqrt{5}} = \\
& \dfrac{2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{3}\cdot \sqrt{5}}{2\cdot \sqrt{3}\cdot \sqrt{5}} = \\
& \dfrac{2\cdot 2\cdot \sqrt{3}\cdot \sqrt{5}}{2\cdot \sqrt{3}\cdot \sqrt{5}} = \\
& 2
\end{aligned}
60
6
⋅
40
=
4
⋅
3
⋅
5
2
⋅
3
⋅
8
⋅
5
=
2
⋅
3
⋅
5
2
⋅
3
⋅
2
⋅
2
⋅
5
=
2
⋅
3
⋅
5
2
⋅
(
2
⋅
2
)
⋅
3
⋅
5
=
2
⋅
3
⋅
5
2
⋅
2
⋅
3
⋅
5
=
2
Ответ:
2
2
2
.
