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Найдите значение выражения
6
2
⋅
4
13
⋅
26
6\sqrt{2}\cdot 4\sqrt{13}\cdot \sqrt{26}
6
2
⋅
4
13
⋅
26
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Решение
6
2
⋅
4
13
⋅
26
=
6
⋅
2
⋅
4
⋅
13
⋅
2
⋅
13
=
6
⋅
4
⋅
2
⋅
13
⋅
2
⋅
13
=
24
⋅
(
2
⋅
2
)
⋅
(
13
⋅
13
)
=
24
⋅
2
⋅
13
=
624
\begin{aligned}
{}& 6\sqrt{2}\cdot 4\sqrt{13}\cdot \sqrt{26} = 6\cdot \sqrt{2}\cdot 4\cdot \sqrt{13}\cdot \sqrt{2\cdot 13} = \\
& 6\cdot 4\cdot \sqrt{2}\cdot \sqrt{13}\cdot \sqrt{2}\cdot \sqrt{13} = \\
& 24\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{13}\cdot\sqrt{13}) = \\
& 24\cdot 2\cdot 13 = 624
\end{aligned}
6
2
⋅
4
13
⋅
26
=
6
⋅
2
⋅
4
⋅
13
⋅
2
⋅
13
=
6
⋅
4
⋅
2
⋅
13
⋅
2
⋅
13
=
24
⋅
(
2
⋅
2
)
⋅
(
13
⋅
13
)
=
24
⋅
2
⋅
13
=
624
Ответ:
624
624
624
.
