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Найдите значение выражения
2
⋅
126
63
\dfrac{\sqrt{2}\cdot \sqrt{126}}{\sqrt{63}}
63
2
⋅
126
Ответ:
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Решение
2
⋅
126
63
=
2
⋅
2
⋅
9
⋅
7
9
⋅
7
=
2
⋅
3
⋅
2
⋅
7
3
⋅
7
=
3
⋅
(
2
⋅
2
)
⋅
7
3
⋅
7
=
3
⋅
2
⋅
7
3
⋅
7
=
2
\begin{aligned}
{}& \dfrac{\sqrt{2}\cdot \sqrt{126}}{\sqrt{63}} = \dfrac{\sqrt{2}\cdot\sqrt{2\cdot 9\cdot 7}}{\sqrt{9\cdot 7}} = \\
& \dfrac{\sqrt{2}\cdot 3\cdot \sqrt{2}\cdot \sqrt{7}}{3\cdot \sqrt{7}} = \\
& \dfrac{3\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{7}}{3\cdot \sqrt{7}} = \\
& \dfrac{3\cdot 2\cdot \sqrt{7}}{3\cdot \sqrt{7}} = 2
\end{aligned}
63
2
⋅
126
=
9
⋅
7
2
⋅
2
⋅
9
⋅
7
=
3
⋅
7
2
⋅
3
⋅
2
⋅
7
=
3
⋅
7
3
⋅
(
2
⋅
2
)
⋅
7
=
3
⋅
7
3
⋅
2
⋅
7
=
2
Ответ:
2
2
2
.
