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Найдите значение выражения
28
⋅
96
42
\dfrac{\sqrt{28}\cdot \sqrt{96}}{\sqrt{42}}
42
28
⋅
96
Ответ:
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Решение
28
⋅
96
42
=
4
⋅
7
⋅
32
⋅
3
2
⋅
3
⋅
7
=
2
⋅
7
⋅
4
⋅
2
⋅
3
2
⋅
3
⋅
7
=
8
⋅
2
⋅
3
⋅
7
2
⋅
3
⋅
7
=
8
\begin{aligned}
{}& \dfrac{\sqrt{28}\cdot \sqrt{96}}{\sqrt{42}} = \dfrac{\sqrt{4\cdot 7}\cdot\sqrt{32\cdot 3}}{\sqrt{2\cdot 3\cdot 7}} = \\
& \dfrac{2\cdot \sqrt{7}\cdot 4\cdot \sqrt{2}\cdot \sqrt{3}}{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{7}} = \\
& \dfrac{8\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{7}}{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{7}} = \\
& 8
\end{aligned}
42
28
⋅
96
=
2
⋅
3
⋅
7
4
⋅
7
⋅
32
⋅
3
=
2
⋅
3
⋅
7
2
⋅
7
⋅
4
⋅
2
⋅
3
=
2
⋅
3
⋅
7
8
⋅
2
⋅
3
⋅
7
=
8
Ответ:
8
8
8
.
