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Найдите значение выражения
72
⋅
122
61
\dfrac{\sqrt{72}\cdot \sqrt{122}}{\sqrt{61}}
61
72
⋅
122
Ответ:
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Решение
72
⋅
122
61
=
8
⋅
9
⋅
2
⋅
61
61
=
6
⋅
2
⋅
2
⋅
61
61
=
6
⋅
(
2
⋅
2
)
⋅
61
61
=
6
⋅
2
⋅
61
61
=
12
\begin{aligned}
{}& \dfrac{\sqrt{72}\cdot \sqrt{122}}{\sqrt{61}} = \dfrac{\sqrt{8\cdot 9}\cdot\sqrt{2\cdot 61}}{\sqrt{61}} = \\
& \dfrac{6\cdot \sqrt{2}\cdot \sqrt{2}\cdot \sqrt{61}}{\sqrt{61}} = \\
& \dfrac{6\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{61}}{\sqrt{61}} = \\
& \dfrac{6\cdot 2\cdot \sqrt{61}}{\sqrt{61}} = 12
\end{aligned}
61
72
⋅
122
=
61
8
⋅
9
⋅
2
⋅
61
=
61
6
⋅
2
⋅
2
⋅
61
=
61
6
⋅
(
2
⋅
2
)
⋅
61
=
61
6
⋅
2
⋅
61
=
12
Ответ:
12
12
12
.
