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Найдите значение выражения
6
⋅
128
48
\dfrac{\sqrt{6}\cdot \sqrt{128}}{\sqrt{48}}
48
6
⋅
128
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Решение
6
⋅
128
48
=
2
⋅
3
⋅
2
7
16
⋅
3
=
2
⋅
3
⋅
8
⋅
2
4
⋅
3
=
8
⋅
(
2
⋅
2
)
⋅
3
4
⋅
3
=
8
⋅
2
⋅
3
4
⋅
3
=
4
\begin{aligned}
{}& \dfrac{\sqrt{6}\cdot \sqrt{128}}{\sqrt{48}} = \dfrac{\sqrt{2\cdot 3}\cdot\sqrt{2^{7}}}{\sqrt{16\cdot 3}} = \\
& \dfrac{\sqrt{2}\cdot \sqrt{3}\cdot 8\cdot \sqrt{2}}{4\cdot \sqrt{3}} = \\
& \dfrac{8\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{3}}{4\cdot \sqrt{3}} = \\
& \dfrac{8\cdot 2\cdot \sqrt{3}}{4\cdot \sqrt{3}} = 4
\end{aligned}
48
6
⋅
128
=
16
⋅
3
2
⋅
3
⋅
2
7
=
4
⋅
3
2
⋅
3
⋅
8
⋅
2
=
4
⋅
3
8
⋅
(
2
⋅
2
)
⋅
3
=
4
⋅
3
8
⋅
2
⋅
3
=
4
Ответ:
4
4
4
.
