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Найдите значение выражения
125
⋅
160
32
\dfrac{\sqrt{125}\cdot \sqrt{160}}{\sqrt{32}}
32
125
⋅
160
Ответ:
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Решение
125
⋅
160
32
=
5
3
⋅
32
⋅
5
2
5
=
5
⋅
5
⋅
4
⋅
2
⋅
5
4
⋅
2
=
20
⋅
2
⋅
(
5
⋅
5
)
4
⋅
2
=
20
⋅
5
⋅
2
4
⋅
2
=
25
\begin{aligned}
{}& \dfrac{\sqrt{125}\cdot \sqrt{160}}{\sqrt{32}} = \dfrac{\sqrt{5^{3}}\cdot\sqrt{32\cdot 5}}{\sqrt{2^{5}}} = \\
& \dfrac{5\cdot \sqrt{5}\cdot 4\cdot \sqrt{2}\cdot \sqrt{5}}{4\cdot \sqrt{2}} = \\
& \dfrac{20\cdot \sqrt{2}\cdot (\sqrt{5}\cdot\sqrt{5})}{4\cdot \sqrt{2}} = \\
& \dfrac{20\cdot 5\cdot \sqrt{2}}{4\cdot \sqrt{2}} = 25
\end{aligned}
32
125
⋅
160
=
2
5
5
3
⋅
32
⋅
5
=
4
⋅
2
5
⋅
5
⋅
4
⋅
2
⋅
5
=
4
⋅
2
20
⋅
2
⋅
(
5
⋅
5
)
=
4
⋅
2
20
⋅
5
⋅
2
=
25
Ответ:
25
25
25
.
