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Найдите значение выражения
2
5
⋅
3
13
⋅
65
2\sqrt{5}\cdot 3\sqrt{13}\cdot \sqrt{65}
2
5
⋅
3
13
⋅
65
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Решение
2
5
⋅
3
13
⋅
65
=
2
⋅
5
⋅
3
⋅
13
⋅
5
⋅
13
=
2
⋅
3
⋅
5
⋅
13
⋅
5
⋅
13
=
6
⋅
(
5
⋅
5
)
⋅
(
13
⋅
13
)
=
6
⋅
5
⋅
13
=
390
\begin{aligned}
{}& 2\sqrt{5}\cdot 3\sqrt{13}\cdot \sqrt{65} = 2\cdot \sqrt{5}\cdot 3\cdot \sqrt{13}\cdot \sqrt{5\cdot 13} = \\
& 2\cdot 3\cdot \sqrt{5}\cdot \sqrt{13}\cdot \sqrt{5}\cdot \sqrt{13} = \\
& 6\cdot (\sqrt{5}\cdot\sqrt{5})\cdot (\sqrt{13}\cdot\sqrt{13}) = \\
& 6\cdot 5\cdot 13 = 390
\end{aligned}
2
5
⋅
3
13
⋅
65
=
2
⋅
5
⋅
3
⋅
13
⋅
5
⋅
13
=
2
⋅
3
⋅
5
⋅
13
⋅
5
⋅
13
=
6
⋅
(
5
⋅
5
)
⋅
(
13
⋅
13
)
=
6
⋅
5
⋅
13
=
390
Ответ:
390
390
390
.
