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Найдите значение выражения
10
⋅
30
⋅
3
\sqrt{10}\cdot \sqrt{30}\cdot \sqrt{3}
10
⋅
30
⋅
3
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Решение
10
⋅
30
⋅
3
=
2
⋅
5
⋅
2
⋅
3
⋅
5
⋅
3
=
2
⋅
5
⋅
2
⋅
3
⋅
5
⋅
3
=
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
5
⋅
5
)
=
2
⋅
3
⋅
5
=
30
\begin{aligned}
{}& \sqrt{10}\cdot \sqrt{30}\cdot \sqrt{3} = \sqrt{2\cdot 5}\cdot \sqrt{2\cdot 3\cdot 5}\cdot \sqrt{3} = \\
& \sqrt{2}\cdot \sqrt{5}\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{5}\cdot \sqrt{3} = \\
& (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{5}\cdot\sqrt{5}) = \\
& 2\cdot 3\cdot 5 = 30
\end{aligned}
10
⋅
30
⋅
3
=
2
⋅
5
⋅
2
⋅
3
⋅
5
⋅
3
=
2
⋅
5
⋅
2
⋅
3
⋅
5
⋅
3
=
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
5
⋅
5
)
=
2
⋅
3
⋅
5
=
30
Ответ:
30
30
30
.
