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010a793a
Найдите значение выражения
3
5
⋅
4
13
⋅
65
3\sqrt{5}\cdot 4\sqrt{13}\cdot \sqrt{65}
3
5
⋅
4
13
⋅
65
Ответ:
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Решение
3
5
⋅
4
13
⋅
65
=
3
⋅
5
⋅
4
⋅
13
⋅
5
⋅
13
=
3
⋅
4
⋅
5
⋅
13
⋅
5
⋅
13
=
12
⋅
(
5
⋅
5
)
⋅
(
13
⋅
13
)
=
12
⋅
5
⋅
13
=
780
\begin{aligned}
{}& 3\sqrt{5}\cdot 4\sqrt{13}\cdot \sqrt{65} = 3\cdot \sqrt{5}\cdot 4\cdot \sqrt{13}\cdot \sqrt{5\cdot 13} = \\
& 3\cdot 4\cdot \sqrt{5}\cdot \sqrt{13}\cdot \sqrt{5}\cdot \sqrt{13} = \\
& 12\cdot (\sqrt{5}\cdot\sqrt{5})\cdot (\sqrt{13}\cdot\sqrt{13}) = \\
& 12\cdot 5\cdot 13 = 780
\end{aligned}
3
5
⋅
4
13
⋅
65
=
3
⋅
5
⋅
4
⋅
13
⋅
5
⋅
13
=
3
⋅
4
⋅
5
⋅
13
⋅
5
⋅
13
=
12
⋅
(
5
⋅
5
)
⋅
(
13
⋅
13
)
=
12
⋅
5
⋅
13
=
780
Ответ:
780
780
780
.
