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4c2632f7
Найдите значение выражения
63
⋅
160
70
\dfrac{\sqrt{63}\cdot \sqrt{160}}{\sqrt{70}}
70
63
⋅
160
Ответ:
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Решение
63
⋅
160
70
=
9
⋅
7
⋅
32
⋅
5
2
⋅
5
⋅
7
=
3
⋅
7
⋅
4
⋅
2
⋅
5
2
⋅
5
⋅
7
=
12
⋅
2
⋅
5
⋅
7
2
⋅
5
⋅
7
=
12
\begin{aligned}
{}& \dfrac{\sqrt{63}\cdot \sqrt{160}}{\sqrt{70}} = \dfrac{\sqrt{9\cdot 7}\cdot\sqrt{32\cdot 5}}{\sqrt{2\cdot 5\cdot 7}} = \\
& \dfrac{3\cdot \sqrt{7}\cdot 4\cdot \sqrt{2}\cdot \sqrt{5}}{\sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}} = \\
& \dfrac{12\cdot \sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}}{\sqrt{2}\cdot \sqrt{5}\cdot \sqrt{7}} = \\
& 12
\end{aligned}
70
63
⋅
160
=
2
⋅
5
⋅
7
9
⋅
7
⋅
32
⋅
5
=
2
⋅
5
⋅
7
3
⋅
7
⋅
4
⋅
2
⋅
5
=
2
⋅
5
⋅
7
12
⋅
2
⋅
5
⋅
7
=
12
Ответ:
12
12
12
.
