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Найдите значение выражения
2
2
⋅
5
13
⋅
26
2\sqrt{2}\cdot 5\sqrt{13}\cdot \sqrt{26}
2
2
⋅
5
13
⋅
26
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Решение
2
2
⋅
5
13
⋅
26
=
2
⋅
2
⋅
5
⋅
13
⋅
2
⋅
13
=
2
⋅
5
⋅
2
⋅
13
⋅
2
⋅
13
=
10
⋅
(
2
⋅
2
)
⋅
(
13
⋅
13
)
=
10
⋅
2
⋅
13
=
260
\begin{aligned}
{}& 2\sqrt{2}\cdot 5\sqrt{13}\cdot \sqrt{26} = 2\cdot \sqrt{2}\cdot 5\cdot \sqrt{13}\cdot \sqrt{2\cdot 13} = \\
& 2\cdot 5\cdot \sqrt{2}\cdot \sqrt{13}\cdot \sqrt{2}\cdot \sqrt{13} = \\
& 10\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{13}\cdot\sqrt{13}) = \\
& 10\cdot 2\cdot 13 = 260
\end{aligned}
2
2
⋅
5
13
⋅
26
=
2
⋅
2
⋅
5
⋅
13
⋅
2
⋅
13
=
2
⋅
5
⋅
2
⋅
13
⋅
2
⋅
13
=
10
⋅
(
2
⋅
2
)
⋅
(
13
⋅
13
)
=
10
⋅
2
⋅
13
=
260
Ответ:
260
260
260
.
