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Найдите значение выражения
4
2
⋅
5
13
⋅
26
4\sqrt{2}\cdot 5\sqrt{13}\cdot \sqrt{26}
4
2
⋅
5
13
⋅
26
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Решение
4
2
⋅
5
13
⋅
26
=
4
⋅
2
⋅
5
⋅
13
⋅
2
⋅
13
=
4
⋅
5
⋅
2
⋅
13
⋅
2
⋅
13
=
20
⋅
(
2
⋅
2
)
⋅
(
13
⋅
13
)
=
20
⋅
2
⋅
13
=
520
\begin{aligned}
{}& 4\sqrt{2}\cdot 5\sqrt{13}\cdot \sqrt{26} = 4\cdot \sqrt{2}\cdot 5\cdot \sqrt{13}\cdot \sqrt{2\cdot 13} = \\
& 4\cdot 5\cdot \sqrt{2}\cdot \sqrt{13}\cdot \sqrt{2}\cdot \sqrt{13} = \\
& 20\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{13}\cdot\sqrt{13}) = \\
& 20\cdot 2\cdot 13 = 520
\end{aligned}
4
2
⋅
5
13
⋅
26
=
4
⋅
2
⋅
5
⋅
13
⋅
2
⋅
13
=
4
⋅
5
⋅
2
⋅
13
⋅
2
⋅
13
=
20
⋅
(
2
⋅
2
)
⋅
(
13
⋅
13
)
=
20
⋅
2
⋅
13
=
520
Ответ:
520
520
520
.
