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415e57d5
Найдите значение выражения
65
⋅
182
70
\dfrac{\sqrt{65}\cdot \sqrt{182}}{\sqrt{70}}
70
65
⋅
182
Ответ:
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Решение
65
⋅
182
70
=
5
⋅
13
⋅
2
⋅
7
⋅
13
2
⋅
5
⋅
7
=
5
⋅
13
⋅
2
⋅
7
⋅
13
2
⋅
5
⋅
7
=
2
⋅
5
⋅
7
⋅
(
13
⋅
13
)
2
⋅
5
⋅
7
=
13
⋅
2
⋅
5
⋅
7
2
⋅
5
⋅
7
=
13
\begin{aligned}
{}& \dfrac{\sqrt{65}\cdot \sqrt{182}}{\sqrt{70}} = \dfrac{\sqrt{5\cdot 13}\cdot\sqrt{2\cdot 7\cdot 13}}{\sqrt{2\cdot 5\cdot 7}} = \\
& \dfrac{\sqrt{5}\cdot \sqrt{13}\cdot \sqrt{2}\cdot \sqrt{7}\cdot \sqrt{13}}{\sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}} = \\
& \dfrac{\sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}\cdot (\sqrt{13}\cdot\sqrt{13})}{\sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}} = \\
& \dfrac{13\cdot \sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}}{\sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}} = \\
& 13
\end{aligned}
70
65
⋅
182
=
2
⋅
5
⋅
7
5
⋅
13
⋅
2
⋅
7
⋅
13
=
2
⋅
5
⋅
7
5
⋅
13
⋅
2
⋅
7
⋅
13
=
2
⋅
5
⋅
7
2
⋅
5
⋅
7
⋅
(
13
⋅
13
)
=
2
⋅
5
⋅
7
13
⋅
2
⋅
5
⋅
7
=
13
Ответ:
13
13
13
.
