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Найдите значение выражения
72
⋅
104
52
\dfrac{\sqrt{72}\cdot \sqrt{104}}{\sqrt{52}}
52
72
⋅
104
Ответ:
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Решение
72
⋅
104
52
=
8
⋅
9
⋅
8
⋅
13
4
⋅
13
=
6
⋅
2
⋅
2
⋅
2
⋅
13
2
⋅
13
=
12
⋅
(
2
⋅
2
)
⋅
13
2
⋅
13
=
12
⋅
2
⋅
13
2
⋅
13
=
12
\begin{aligned}
{}& \dfrac{\sqrt{72}\cdot \sqrt{104}}{\sqrt{52}} = \dfrac{\sqrt{8\cdot 9}\cdot\sqrt{8\cdot 13}}{\sqrt{4\cdot 13}} = \\
& \dfrac{6\cdot \sqrt{2}\cdot 2\cdot \sqrt{2}\cdot \sqrt{13}}{2\cdot \sqrt{13}} = \\
& \dfrac{12\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{13}}{2\cdot \sqrt{13}} = \\
& \dfrac{12\cdot 2\cdot \sqrt{13}}{2\cdot \sqrt{13}} = 12
\end{aligned}
52
72
⋅
104
=
4
⋅
13
8
⋅
9
⋅
8
⋅
13
=
2
⋅
13
6
⋅
2
⋅
2
⋅
2
⋅
13
=
2
⋅
13
12
⋅
(
2
⋅
2
)
⋅
13
=
2
⋅
13
12
⋅
2
⋅
13
=
12
Ответ:
12
12
12
.
