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Найдите значение выражения
27
⋅
30
⋅
10
\sqrt{27}\cdot \sqrt{30}\cdot \sqrt{10}
27
⋅
30
⋅
10
Ответ:
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Решение
27
⋅
30
⋅
10
=
3
3
⋅
2
⋅
3
⋅
5
⋅
2
⋅
5
=
3
⋅
3
⋅
2
⋅
3
⋅
5
⋅
2
⋅
5
=
3
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
5
⋅
5
)
=
3
⋅
2
⋅
3
⋅
5
=
90
\begin{aligned}
{}& \sqrt{27}\cdot \sqrt{30}\cdot \sqrt{10} = \sqrt{3^{3}}\cdot \sqrt{2\cdot 3\cdot 5}\cdot \sqrt{2\cdot 5} = \\
& 3\cdot \sqrt{3}\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{5}\cdot \sqrt{2}\cdot \sqrt{5} = \\
& 3\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{5}\cdot\sqrt{5}) = \\
& 3\cdot 2\cdot 3\cdot 5 = 90
\end{aligned}
27
⋅
30
⋅
10
=
3
3
⋅
2
⋅
3
⋅
5
⋅
2
⋅
5
=
3
⋅
3
⋅
2
⋅
3
⋅
5
⋅
2
⋅
5
=
3
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
5
⋅
5
)
=
3
⋅
2
⋅
3
⋅
5
=
90
Ответ:
90
90
90
.
