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Найдите значение выражения
6
⋅
27
⋅
50
\sqrt{6}\cdot \sqrt{27}\cdot \sqrt{50}
6
⋅
27
⋅
50
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Решение
6
⋅
27
⋅
50
=
2
⋅
3
⋅
3
3
⋅
2
⋅
25
=
2
⋅
3
⋅
3
⋅
3
⋅
5
⋅
2
=
15
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
15
⋅
2
⋅
3
=
90
\begin{aligned}
{}& \sqrt{6}\cdot \sqrt{27}\cdot \sqrt{50} = \sqrt{2\cdot 3}\cdot \sqrt{3^{3}}\cdot \sqrt{2\cdot 25} = \\
& \sqrt{2}\cdot \sqrt{3}\cdot 3\cdot \sqrt{3}\cdot 5\cdot \sqrt{2} = \\
& 15\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 15\cdot 2\cdot 3 = 90
\end{aligned}
6
⋅
27
⋅
50
=
2
⋅
3
⋅
3
3
⋅
2
⋅
25
=
2
⋅
3
⋅
3
⋅
3
⋅
5
⋅
2
=
15
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
15
⋅
2
⋅
3
=
90
Ответ:
90
90
90
.
