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Найдите значение выражения
5
2
⋅
5
13
⋅
26
5\sqrt{2}\cdot 5\sqrt{13}\cdot \sqrt{26}
5
2
⋅
5
13
⋅
26
Ответ:
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Решение
5
2
⋅
5
13
⋅
26
=
5
⋅
2
⋅
5
⋅
13
⋅
2
⋅
13
=
5
⋅
5
⋅
2
⋅
13
⋅
2
⋅
13
=
25
⋅
(
2
⋅
2
)
⋅
(
13
⋅
13
)
=
25
⋅
2
⋅
13
=
650
\begin{aligned}
{}& 5\sqrt{2}\cdot 5\sqrt{13}\cdot \sqrt{26} = 5\cdot \sqrt{2}\cdot 5\cdot \sqrt{13}\cdot \sqrt{2\cdot 13} = \\
& 5\cdot 5\cdot \sqrt{2}\cdot \sqrt{13}\cdot \sqrt{2}\cdot \sqrt{13} = \\
& 25\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{13}\cdot\sqrt{13}) = \\
& 25\cdot 2\cdot 13 = 650
\end{aligned}
5
2
⋅
5
13
⋅
26
=
5
⋅
2
⋅
5
⋅
13
⋅
2
⋅
13
=
5
⋅
5
⋅
2
⋅
13
⋅
2
⋅
13
=
25
⋅
(
2
⋅
2
)
⋅
(
13
⋅
13
)
=
25
⋅
2
⋅
13
=
650
Ответ:
650
650
650
.
