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Найдите значение выражения
4
7
⋅
2
11
⋅
77
4\sqrt{7}\cdot 2\sqrt{11}\cdot \sqrt{77}
4
7
⋅
2
11
⋅
77
Ответ:
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Решение
4
7
⋅
2
11
⋅
77
=
4
⋅
7
⋅
2
⋅
11
⋅
7
⋅
11
=
4
⋅
2
⋅
7
⋅
11
⋅
7
⋅
11
=
8
⋅
(
7
⋅
7
)
⋅
(
11
⋅
11
)
=
8
⋅
7
⋅
11
=
616
\begin{aligned}
{}& 4\sqrt{7}\cdot 2\sqrt{11}\cdot \sqrt{77} = 4\cdot \sqrt{7}\cdot 2\cdot \sqrt{11}\cdot \sqrt{7\cdot 11} = \\
& 4\cdot 2\cdot \sqrt{7}\cdot \sqrt{11}\cdot \sqrt{7}\cdot \sqrt{11} = \\
& 8\cdot (\sqrt{7}\cdot\sqrt{7})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 8\cdot 7\cdot 11 = 616
\end{aligned}
4
7
⋅
2
11
⋅
77
=
4
⋅
7
⋅
2
⋅
11
⋅
7
⋅
11
=
4
⋅
2
⋅
7
⋅
11
⋅
7
⋅
11
=
8
⋅
(
7
⋅
7
)
⋅
(
11
⋅
11
)
=
8
⋅
7
⋅
11
=
616
Ответ:
616
616
616
.
