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Найдите значение выражения
96
⋅
176
66
\dfrac{\sqrt{96}\cdot \sqrt{176}}{\sqrt{66}}
66
96
⋅
176
Ответ:
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Решение
96
⋅
176
66
=
32
⋅
3
⋅
16
⋅
11
2
⋅
3
⋅
11
=
4
⋅
2
⋅
3
⋅
4
⋅
11
2
⋅
3
⋅
11
=
16
⋅
2
⋅
3
⋅
11
2
⋅
3
⋅
11
=
16
\begin{aligned}
{}& \dfrac{\sqrt{96}\cdot \sqrt{176}}{\sqrt{66}} = \dfrac{\sqrt{32\cdot 3}\cdot\sqrt{16\cdot 11}}{\sqrt{2\cdot 3\cdot 11}} = \\
& \dfrac{4\cdot \sqrt{2}\cdot \sqrt{3}\cdot 4\cdot \sqrt{11}}{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{11}} = \\
& \dfrac{16\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{11}}{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{11}} = \\
& 16
\end{aligned}
66
96
⋅
176
=
2
⋅
3
⋅
11
32
⋅
3
⋅
16
⋅
11
=
2
⋅
3
⋅
11
4
⋅
2
⋅
3
⋅
4
⋅
11
=
2
⋅
3
⋅
11
16
⋅
2
⋅
3
⋅
11
=
16
Ответ:
16
16
16
.
