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Найдите значение выражения
35
⋅
72
70
\dfrac{\sqrt{35}\cdot \sqrt{72}}{\sqrt{70}}
70
35
⋅
72
Ответ:
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Решение
35
⋅
72
70
=
5
⋅
7
⋅
8
⋅
9
2
⋅
5
⋅
7
=
5
⋅
7
⋅
6
⋅
2
2
⋅
5
⋅
7
=
6
⋅
2
⋅
5
⋅
7
2
⋅
5
⋅
7
=
6
\begin{aligned}
{}& \dfrac{\sqrt{35}\cdot \sqrt{72}}{\sqrt{70}} = \dfrac{\sqrt{5\cdot 7}\cdot\sqrt{8\cdot 9}}{\sqrt{2\cdot 5\cdot 7}} = \\
& \dfrac{\sqrt{5}\cdot \sqrt{7}\cdot 6\cdot \sqrt{2}}{\sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}} = \\
& \dfrac{6\cdot \sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}}{\sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}} = \\
& 6
\end{aligned}
70
35
⋅
72
=
2
⋅
5
⋅
7
5
⋅
7
⋅
8
⋅
9
=
2
⋅
5
⋅
7
5
⋅
7
⋅
6
⋅
2
=
2
⋅
5
⋅
7
6
⋅
2
⋅
5
⋅
7
=
6
Ответ:
6
6
6
.
