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Найдите значение выражения
3
⋅
138
46
\dfrac{\sqrt{3}\cdot \sqrt{138}}{\sqrt{46}}
46
3
⋅
138
Ответ:
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Решение
3
⋅
138
46
=
3
⋅
2
⋅
3
⋅
23
2
⋅
23
=
3
⋅
2
⋅
3
⋅
23
2
⋅
23
=
2
⋅
(
3
⋅
3
)
⋅
23
2
⋅
23
=
3
⋅
2
⋅
23
2
⋅
23
=
3
\begin{aligned}
{}& \dfrac{\sqrt{3}\cdot \sqrt{138}}{\sqrt{46}} = \dfrac{\sqrt{3}\cdot\sqrt{2\cdot 3\cdot 23}}{\sqrt{2\cdot 23}} = \\
& \dfrac{\sqrt{3}\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{23}}{\sqrt{2}\cdot \sqrt{23}} = \\
& \dfrac{\sqrt{2}\cdot (\sqrt{3}\cdot\sqrt{3})\cdot \sqrt{23}}{\sqrt{2}\cdot \sqrt{23}} = \\
& \dfrac{3\cdot \sqrt{2}\cdot \sqrt{23}}{\sqrt{2}\cdot \sqrt{23}} = \\
& 3
\end{aligned}
46
3
⋅
138
=
2
⋅
23
3
⋅
2
⋅
3
⋅
23
=
2
⋅
23
3
⋅
2
⋅
3
⋅
23
=
2
⋅
23
2
⋅
(
3
⋅
3
)
⋅
23
=
2
⋅
23
3
⋅
2
⋅
23
=
3
Ответ:
3
3
3
.
