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Найдите значение выражения
18
⋅
120
60
\dfrac{\sqrt{18}\cdot \sqrt{120}}{\sqrt{60}}
60
18
⋅
120
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Решение
18
⋅
120
60
=
2
⋅
9
⋅
8
⋅
3
⋅
5
4
⋅
3
⋅
5
=
3
⋅
2
⋅
2
⋅
2
⋅
3
⋅
5
2
⋅
3
⋅
5
=
6
⋅
(
2
⋅
2
)
⋅
3
⋅
5
2
⋅
3
⋅
5
=
6
⋅
2
⋅
3
⋅
5
2
⋅
3
⋅
5
=
6
\begin{aligned}
{}& \dfrac{\sqrt{18}\cdot \sqrt{120}}{\sqrt{60}} = \dfrac{\sqrt{2\cdot 9}\cdot\sqrt{8\cdot 3\cdot 5}}{\sqrt{4\cdot 3\cdot 5}} = \\
& \dfrac{3\cdot \sqrt{2}\cdot 2\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{5}}{2\cdot \sqrt{3}\cdot \sqrt{5}} = \\
& \dfrac{6\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{3}\cdot \sqrt{5}}{2\cdot \sqrt{3}\cdot \sqrt{5}} = \\
& \dfrac{6\cdot 2\cdot \sqrt{3}\cdot \sqrt{5}}{2\cdot \sqrt{3}\cdot \sqrt{5}} = \\
& 6
\end{aligned}
60
18
⋅
120
=
4
⋅
3
⋅
5
2
⋅
9
⋅
8
⋅
3
⋅
5
=
2
⋅
3
⋅
5
3
⋅
2
⋅
2
⋅
2
⋅
3
⋅
5
=
2
⋅
3
⋅
5
6
⋅
(
2
⋅
2
)
⋅
3
⋅
5
=
2
⋅
3
⋅
5
6
⋅
2
⋅
3
⋅
5
=
6
Ответ:
6
6
6
.
