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Найдите значение выражения
5
⋅
8
⋅
10
\sqrt{5}\cdot \sqrt{8}\cdot \sqrt{10}
5
⋅
8
⋅
10
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Решение
5
⋅
8
⋅
10
=
5
⋅
2
3
⋅
2
⋅
5
=
5
⋅
2
⋅
2
⋅
2
⋅
5
=
2
⋅
(
2
⋅
2
)
⋅
(
5
⋅
5
)
=
2
⋅
2
⋅
5
=
20
\begin{aligned}
{}& \sqrt{5}\cdot \sqrt{8}\cdot \sqrt{10} = \sqrt{5}\cdot \sqrt{2^{3}}\cdot \sqrt{2\cdot 5} = \\
& \sqrt{5}\cdot 2\cdot \sqrt{2}\cdot \sqrt{2}\cdot \sqrt{5} = \\
& 2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{5}\cdot\sqrt{5}) = \\
& 2\cdot 2\cdot 5 = 20
\end{aligned}
5
⋅
8
⋅
10
=
5
⋅
2
3
⋅
2
⋅
5
=
5
⋅
2
⋅
2
⋅
2
⋅
5
=
2
⋅
(
2
⋅
2
)
⋅
(
5
⋅
5
)
=
2
⋅
2
⋅
5
=
20
Ответ:
20
20
20
.
