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Найдите значение выражения
8
⋅
24
48
\dfrac{\sqrt{8}\cdot \sqrt{24}}{\sqrt{48}}
48
8
⋅
24
Ответ:
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Решение
8
⋅
24
48
=
2
3
⋅
8
⋅
3
16
⋅
3
=
2
⋅
2
⋅
2
⋅
2
⋅
3
4
⋅
3
=
4
⋅
(
2
⋅
2
)
⋅
3
4
⋅
3
=
4
⋅
2
⋅
3
4
⋅
3
=
2
\begin{aligned}
{}& \dfrac{\sqrt{8}\cdot \sqrt{24}}{\sqrt{48}} = \dfrac{\sqrt{2^{3}}\cdot\sqrt{8\cdot 3}}{\sqrt{16\cdot 3}} = \\
& \dfrac{2\cdot \sqrt{2}\cdot 2\cdot \sqrt{2}\cdot \sqrt{3}}{4\cdot \sqrt{3}} = \\
& \dfrac{4\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{3}}{4\cdot \sqrt{3}} = \\
& \dfrac{4\cdot 2\cdot \sqrt{3}}{4\cdot \sqrt{3}} = 2
\end{aligned}
48
8
⋅
24
=
16
⋅
3
2
3
⋅
8
⋅
3
=
4
⋅
3
2
⋅
2
⋅
2
⋅
2
⋅
3
=
4
⋅
3
4
⋅
(
2
⋅
2
)
⋅
3
=
4
⋅
3
4
⋅
2
⋅
3
=
2
Ответ:
2
2
2
.
