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Найдите значение выражения
90
⋅
128
20
\dfrac{\sqrt{90}\cdot \sqrt{128}}{\sqrt{20}}
20
90
⋅
128
Ответ:
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Решение
90
⋅
128
20
=
2
⋅
9
⋅
5
⋅
2
7
4
⋅
5
=
3
⋅
2
⋅
5
⋅
8
⋅
2
2
⋅
5
=
24
⋅
(
2
⋅
2
)
⋅
5
2
⋅
5
=
24
⋅
2
⋅
5
2
⋅
5
=
24
\begin{aligned}
{}& \dfrac{\sqrt{90}\cdot \sqrt{128}}{\sqrt{20}} = \dfrac{\sqrt{2\cdot 9\cdot 5}\cdot\sqrt{2^{7}}}{\sqrt{4\cdot 5}} = \\
& \dfrac{3\cdot \sqrt{2}\cdot \sqrt{5}\cdot 8\cdot \sqrt{2}}{2\cdot \sqrt{5}} = \\
& \dfrac{24\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{5}}{2\cdot \sqrt{5}} = \\
& \dfrac{24\cdot 2\cdot \sqrt{5}}{2\cdot \sqrt{5}} = 24
\end{aligned}
20
90
⋅
128
=
4
⋅
5
2
⋅
9
⋅
5
⋅
2
7
=
2
⋅
5
3
⋅
2
⋅
5
⋅
8
⋅
2
=
2
⋅
5
24
⋅
(
2
⋅
2
)
⋅
5
=
2
⋅
5
24
⋅
2
⋅
5
=
24
Ответ:
24
24
24
.
