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Найдите значение выражения
18
⋅
90
⋅
5
\sqrt{18}\cdot \sqrt{90}\cdot \sqrt{5}
18
⋅
90
⋅
5
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Решение
18
⋅
90
⋅
5
=
2
⋅
9
⋅
2
⋅
9
⋅
5
⋅
5
=
3
⋅
2
⋅
3
⋅
2
⋅
5
⋅
5
=
9
⋅
(
2
⋅
2
)
⋅
(
5
⋅
5
)
=
9
⋅
2
⋅
5
=
90
\begin{aligned}
{}& \sqrt{18}\cdot \sqrt{90}\cdot \sqrt{5} = \sqrt{2\cdot 9}\cdot \sqrt{2\cdot 9\cdot 5}\cdot \sqrt{5} = \\
& 3\cdot \sqrt{2}\cdot 3\cdot \sqrt{2}\cdot \sqrt{5}\cdot \sqrt{5} = \\
& 9\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{5}\cdot\sqrt{5}) = \\
& 9\cdot 2\cdot 5 = 90
\end{aligned}
18
⋅
90
⋅
5
=
2
⋅
9
⋅
2
⋅
9
⋅
5
⋅
5
=
3
⋅
2
⋅
3
⋅
2
⋅
5
⋅
5
=
9
⋅
(
2
⋅
2
)
⋅
(
5
⋅
5
)
=
9
⋅
2
⋅
5
=
90
Ответ:
90
90
90
.
