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Найдите значение выражения
154
⋅
162
77
\dfrac{\sqrt{154}\cdot \sqrt{162}}{\sqrt{77}}
77
154
⋅
162
Ответ:
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Решение
154
⋅
162
77
=
2
⋅
7
⋅
11
⋅
2
⋅
81
7
⋅
11
=
2
⋅
7
⋅
11
⋅
9
⋅
2
7
⋅
11
=
9
⋅
(
2
⋅
2
)
⋅
7
⋅
11
7
⋅
11
=
9
⋅
2
⋅
7
⋅
11
7
⋅
11
=
18
\begin{aligned}
{}& \dfrac{\sqrt{154}\cdot \sqrt{162}}{\sqrt{77}} = \dfrac{\sqrt{2\cdot 7\cdot 11}\cdot\sqrt{2\cdot 81}}{\sqrt{7\cdot 11}} = \\
& \dfrac{\sqrt{2}\cdot \sqrt{7}\cdot \sqrt{11}\cdot 9\cdot \sqrt{2}}{\sqrt{7}\cdot \sqrt{11}} = \\
& \dfrac{9\cdot (\sqrt{2}\cdot\sqrt{2})\cdot \sqrt{7}\cdot \sqrt{11}}{\sqrt{7}\cdot \sqrt{11}} = \\
& \dfrac{9\cdot 2\cdot \sqrt{7}\cdot \sqrt{11}}{\sqrt{7}\cdot \sqrt{11}} = \\
& 18
\end{aligned}
77
154
⋅
162
=
7
⋅
11
2
⋅
7
⋅
11
⋅
2
⋅
81
=
7
⋅
11
2
⋅
7
⋅
11
⋅
9
⋅
2
=
7
⋅
11
9
⋅
(
2
⋅
2
)
⋅
7
⋅
11
=
7
⋅
11
9
⋅
2
⋅
7
⋅
11
=
18
Ответ:
18
18
18
.
