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Найдите значение выражения
11
⋅
154
14
\dfrac{\sqrt{11}\cdot \sqrt{154}}{\sqrt{14}}
14
11
⋅
154
Ответ:
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Решение
11
⋅
154
14
=
11
⋅
2
⋅
7
⋅
11
2
⋅
7
=
11
⋅
2
⋅
7
⋅
11
2
⋅
7
=
2
⋅
7
⋅
(
11
⋅
11
)
2
⋅
7
=
11
⋅
2
⋅
7
2
⋅
7
=
11
\begin{aligned}
{}& \dfrac{\sqrt{11}\cdot \sqrt{154}}{\sqrt{14}} = \dfrac{\sqrt{11}\cdot\sqrt{2\cdot 7\cdot 11}}{\sqrt{2\cdot 7}} = \\
& \dfrac{\sqrt{11}\cdot \sqrt{2}\cdot \sqrt{7}\cdot \sqrt{11}}{\sqrt{2}\cdot \sqrt{7}} = \\
& \dfrac{\sqrt{2}\cdot \sqrt{7}\cdot (\sqrt{11}\cdot\sqrt{11})}{\sqrt{2}\cdot \sqrt{7}} = \\
& \dfrac{11\cdot \sqrt{2}\cdot \sqrt{7}}{\sqrt{2}\cdot \sqrt{7}} = \\
& 11
\end{aligned}
14
11
⋅
154
=
2
⋅
7
11
⋅
2
⋅
7
⋅
11
=
2
⋅
7
11
⋅
2
⋅
7
⋅
11
=
2
⋅
7
2
⋅
7
⋅
(
11
⋅
11
)
=
2
⋅
7
11
⋅
2
⋅
7
=
11
Ответ:
11
11
11
.
