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498e8599
Найдите значение выражения
3
7
⋅
3
11
⋅
77
3\sqrt{7}\cdot 3\sqrt{11}\cdot \sqrt{77}
3
7
⋅
3
11
⋅
77
Ответ:
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Решение
3
7
⋅
3
11
⋅
77
=
3
⋅
7
⋅
3
⋅
11
⋅
7
⋅
11
=
3
⋅
3
⋅
7
⋅
11
⋅
7
⋅
11
=
9
⋅
(
7
⋅
7
)
⋅
(
11
⋅
11
)
=
9
⋅
7
⋅
11
=
693
\begin{aligned}
{}& 3\sqrt{7}\cdot 3\sqrt{11}\cdot \sqrt{77} = 3\cdot \sqrt{7}\cdot 3\cdot \sqrt{11}\cdot \sqrt{7\cdot 11} = \\
& 3\cdot 3\cdot \sqrt{7}\cdot \sqrt{11}\cdot \sqrt{7}\cdot \sqrt{11} = \\
& 9\cdot (\sqrt{7}\cdot\sqrt{7})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 9\cdot 7\cdot 11 = 693
\end{aligned}
3
7
⋅
3
11
⋅
77
=
3
⋅
7
⋅
3
⋅
11
⋅
7
⋅
11
=
3
⋅
3
⋅
7
⋅
11
⋅
7
⋅
11
=
9
⋅
(
7
⋅
7
)
⋅
(
11
⋅
11
)
=
9
⋅
7
⋅
11
=
693
Ответ:
693
693
693
.
