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Найдите значение выражения
6
2
⋅
4
17
⋅
34
6\sqrt{2}\cdot 4\sqrt{17}\cdot \sqrt{34}
6
2
⋅
4
17
⋅
34
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Решение
6
2
⋅
4
17
⋅
34
=
6
⋅
2
⋅
4
⋅
17
⋅
2
⋅
17
=
6
⋅
4
⋅
2
⋅
17
⋅
2
⋅
17
=
24
⋅
(
2
⋅
2
)
⋅
(
17
⋅
17
)
=
24
⋅
2
⋅
17
=
816
\begin{aligned}
{}& 6\sqrt{2}\cdot 4\sqrt{17}\cdot \sqrt{34} = 6\cdot \sqrt{2}\cdot 4\cdot \sqrt{17}\cdot \sqrt{2\cdot 17} = \\
& 6\cdot 4\cdot \sqrt{2}\cdot \sqrt{17}\cdot \sqrt{2}\cdot \sqrt{17} = \\
& 24\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{17}\cdot\sqrt{17}) = \\
& 24\cdot 2\cdot 17 = 816
\end{aligned}
6
2
⋅
4
17
⋅
34
=
6
⋅
2
⋅
4
⋅
17
⋅
2
⋅
17
=
6
⋅
4
⋅
2
⋅
17
⋅
2
⋅
17
=
24
⋅
(
2
⋅
2
)
⋅
(
17
⋅
17
)
=
24
⋅
2
⋅
17
=
816
Ответ:
816
816
816
.
