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26e1415d
Найдите значение выражения
96
⋅
138
23
\dfrac{\sqrt{96}\cdot \sqrt{138}}{\sqrt{23}}
23
96
⋅
138
Ответ:
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Решение
96
⋅
138
23
=
32
⋅
3
⋅
2
⋅
3
⋅
23
23
=
4
⋅
2
⋅
3
⋅
2
⋅
3
⋅
23
23
=
4
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
23
23
=
4
⋅
2
⋅
3
⋅
23
23
=
24
\begin{aligned}
{}& \dfrac{\sqrt{96}\cdot \sqrt{138}}{\sqrt{23}} = \dfrac{\sqrt{32\cdot 3}\cdot\sqrt{2\cdot 3\cdot 23}}{\sqrt{23}} = \\
& \dfrac{4\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{23}}{\sqrt{23}} = \\
& \dfrac{4\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3})\cdot \sqrt{23}}{\sqrt{23}} = \\
& \dfrac{4\cdot 2\cdot 3\cdot \sqrt{23}}{\sqrt{23}} = 24
\end{aligned}
23
96
⋅
138
=
23
32
⋅
3
⋅
2
⋅
3
⋅
23
=
23
4
⋅
2
⋅
3
⋅
2
⋅
3
⋅
23
=
23
4
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
23
=
23
4
⋅
2
⋅
3
⋅
23
=
24
Ответ:
24
24
24
.
