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Найдите значение выражения
50
⋅
75
⋅
6
\sqrt{50}\cdot \sqrt{75}\cdot \sqrt{6}
50
⋅
75
⋅
6
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Решение
50
⋅
75
⋅
6
=
2
⋅
25
⋅
3
⋅
25
⋅
2
⋅
3
=
5
⋅
2
⋅
5
⋅
3
⋅
2
⋅
3
=
25
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
25
⋅
2
⋅
3
=
150
\begin{aligned}
{}& \sqrt{50}\cdot \sqrt{75}\cdot \sqrt{6} = \sqrt{2\cdot 25}\cdot \sqrt{3\cdot 25}\cdot \sqrt{2\cdot 3} = \\
& 5\cdot \sqrt{2}\cdot 5\cdot \sqrt{3}\cdot \sqrt{2}\cdot \sqrt{3} = \\
& 25\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 25\cdot 2\cdot 3 = 150
\end{aligned}
50
⋅
75
⋅
6
=
2
⋅
25
⋅
3
⋅
25
⋅
2
⋅
3
=
5
⋅
2
⋅
5
⋅
3
⋅
2
⋅
3
=
25
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
25
⋅
2
⋅
3
=
150
Ответ:
150
150
150
.
