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Найдите значение выражения
88
⋅
110
20
\dfrac{\sqrt{88}\cdot \sqrt{110}}{\sqrt{20}}
20
88
⋅
110
Ответ:
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Решение
88
⋅
110
20
=
8
⋅
11
⋅
2
⋅
5
⋅
11
4
⋅
5
=
2
⋅
2
⋅
11
⋅
2
⋅
5
⋅
11
2
⋅
5
=
2
⋅
(
2
⋅
2
)
⋅
5
⋅
(
11
⋅
11
)
2
⋅
5
=
2
⋅
2
⋅
11
⋅
5
2
⋅
5
=
22
\begin{aligned}
{}& \dfrac{\sqrt{88}\cdot \sqrt{110}}{\sqrt{20}} = \dfrac{\sqrt{8\cdot 11}\cdot\sqrt{2\cdot 5\cdot 11}}{\sqrt{4\cdot 5}} = \\
& \dfrac{2\cdot \sqrt{2}\cdot \sqrt{11}\cdot \sqrt{2}\cdot \sqrt{5}\cdot \sqrt{11}}{2\cdot \sqrt{5}} = \\
& \dfrac{2\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{5}\cdot (\sqrt{11}\cdot\sqrt{11})}{2\cdot \sqrt{5}} = \\
& \dfrac{2\cdot 2\cdot 11\cdot \sqrt{5}}{2\cdot \sqrt{5}} = \\
& 22
\end{aligned}
20
88
⋅
110
=
4
⋅
5
8
⋅
11
⋅
2
⋅
5
⋅
11
=
2
⋅
5
2
⋅
2
⋅
11
⋅
2
⋅
5
⋅
11
=
2
⋅
5
2
⋅
(
2
⋅
2
)
⋅
5
⋅
(
11
⋅
11
)
=
2
⋅
5
2
⋅
2
⋅
11
⋅
5
=
22
Ответ:
22
22
22
.
