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0e93d75f
Найдите значение выражения
68
⋅
187
44
\dfrac{\sqrt{68}\cdot \sqrt{187}}{\sqrt{44}}
44
68
⋅
187
Ответ:
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Решение
68
⋅
187
44
=
4
⋅
17
⋅
11
⋅
17
4
⋅
11
=
2
⋅
17
⋅
11
⋅
17
2
⋅
11
=
2
⋅
11
⋅
(
17
⋅
17
)
2
⋅
11
=
2
⋅
17
⋅
11
2
⋅
11
=
17
\begin{aligned}
{}& \dfrac{\sqrt{68}\cdot \sqrt{187}}{\sqrt{44}} = \dfrac{\sqrt{4\cdot 17}\cdot\sqrt{11\cdot 17}}{\sqrt{4\cdot 11}} = \\
& \dfrac{2\cdot \sqrt{17}\cdot \sqrt{11}\cdot \sqrt{17}}{2\cdot \sqrt{11}} = \\
& \dfrac{2\cdot \sqrt{11}\cdot (\sqrt{17}\cdot\sqrt{17})}{2\cdot \sqrt{11}} = \\
& \dfrac{2\cdot 17\cdot \sqrt{11}}{2\cdot \sqrt{11}} = 17
\end{aligned}
44
68
⋅
187
=
4
⋅
11
4
⋅
17
⋅
11
⋅
17
=
2
⋅
11
2
⋅
17
⋅
11
⋅
17
=
2
⋅
11
2
⋅
11
⋅
(
17
⋅
17
)
=
2
⋅
11
2
⋅
17
⋅
11
=
17
Ответ:
17
17
17
.
