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Найдите значение выражения
8
⋅
75
⋅
24
\sqrt{8}\cdot \sqrt{75}\cdot \sqrt{24}
8
⋅
75
⋅
24
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Решение
8
⋅
75
⋅
24
=
2
3
⋅
3
⋅
25
⋅
8
⋅
3
=
2
⋅
2
⋅
5
⋅
3
⋅
2
⋅
2
⋅
3
=
20
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
20
⋅
2
⋅
3
=
120
\begin{aligned}
{}& \sqrt{8}\cdot \sqrt{75}\cdot \sqrt{24} = \sqrt{2^{3}}\cdot \sqrt{3\cdot 25}\cdot \sqrt{8\cdot 3} = \\
& 2\cdot \sqrt{2}\cdot 5\cdot \sqrt{3}\cdot 2\cdot \sqrt{2}\cdot \sqrt{3} = \\
& 20\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 20\cdot 2\cdot 3 = 120
\end{aligned}
8
⋅
75
⋅
24
=
2
3
⋅
3
⋅
25
⋅
8
⋅
3
=
2
⋅
2
⋅
5
⋅
3
⋅
2
⋅
2
⋅
3
=
20
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
20
⋅
2
⋅
3
=
120
Ответ:
120
120
120
.
