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Найдите значение выражения
4
5
⋅
2
13
⋅
65
4\sqrt{5}\cdot 2\sqrt{13}\cdot \sqrt{65}
4
5
⋅
2
13
⋅
65
Ответ:
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Решение
4
5
⋅
2
13
⋅
65
=
4
⋅
5
⋅
2
⋅
13
⋅
5
⋅
13
=
4
⋅
2
⋅
5
⋅
13
⋅
5
⋅
13
=
8
⋅
(
5
⋅
5
)
⋅
(
13
⋅
13
)
=
8
⋅
5
⋅
13
=
520
\begin{aligned}
{}& 4\sqrt{5}\cdot 2\sqrt{13}\cdot \sqrt{65} = 4\cdot \sqrt{5}\cdot 2\cdot \sqrt{13}\cdot \sqrt{5\cdot 13} = \\
& 4\cdot 2\cdot \sqrt{5}\cdot \sqrt{13}\cdot \sqrt{5}\cdot \sqrt{13} = \\
& 8\cdot (\sqrt{5}\cdot\sqrt{5})\cdot (\sqrt{13}\cdot\sqrt{13}) = \\
& 8\cdot 5\cdot 13 = 520
\end{aligned}
4
5
⋅
2
13
⋅
65
=
4
⋅
5
⋅
2
⋅
13
⋅
5
⋅
13
=
4
⋅
2
⋅
5
⋅
13
⋅
5
⋅
13
=
8
⋅
(
5
⋅
5
)
⋅
(
13
⋅
13
)
=
8
⋅
5
⋅
13
=
520
Ответ:
520
520
520
.
