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Найдите значение выражения
6
⋅
10
⋅
60
\sqrt{6}\cdot \sqrt{10}\cdot \sqrt{60}
6
⋅
10
⋅
60
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Решение
6
⋅
10
⋅
60
=
2
⋅
3
⋅
2
⋅
5
⋅
4
⋅
3
⋅
5
=
2
⋅
3
⋅
2
⋅
5
⋅
2
⋅
3
⋅
5
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
5
⋅
5
)
=
2
⋅
2
⋅
3
⋅
5
=
60
\begin{aligned}
{}& \sqrt{6}\cdot \sqrt{10}\cdot \sqrt{60} = \sqrt{2\cdot 3}\cdot \sqrt{2\cdot 5}\cdot \sqrt{4\cdot 3\cdot 5} = \\
& \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{2}\cdot \sqrt{5}\cdot 2\cdot \sqrt{3}\cdot \sqrt{5} = \\
& 2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{5}\cdot\sqrt{5}) = \\
& 2\cdot 2\cdot 3\cdot 5 = 60
\end{aligned}
6
⋅
10
⋅
60
=
2
⋅
3
⋅
2
⋅
5
⋅
4
⋅
3
⋅
5
=
2
⋅
3
⋅
2
⋅
5
⋅
2
⋅
3
⋅
5
=
2
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
5
⋅
5
)
=
2
⋅
2
⋅
3
⋅
5
=
60
Ответ:
60
60
60
.
