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Найдите значение выражения
2
2
⋅
5
17
⋅
34
2\sqrt{2}\cdot 5\sqrt{17}\cdot \sqrt{34}
2
2
⋅
5
17
⋅
34
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Решение
2
2
⋅
5
17
⋅
34
=
2
⋅
2
⋅
5
⋅
17
⋅
2
⋅
17
=
2
⋅
5
⋅
2
⋅
17
⋅
2
⋅
17
=
10
⋅
(
2
⋅
2
)
⋅
(
17
⋅
17
)
=
10
⋅
2
⋅
17
=
340
\begin{aligned}
{}& 2\sqrt{2}\cdot 5\sqrt{17}\cdot \sqrt{34} = 2\cdot \sqrt{2}\cdot 5\cdot \sqrt{17}\cdot \sqrt{2\cdot 17} = \\
& 2\cdot 5\cdot \sqrt{2}\cdot \sqrt{17}\cdot \sqrt{2}\cdot \sqrt{17} = \\
& 10\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{17}\cdot\sqrt{17}) = \\
& 10\cdot 2\cdot 17 = 340
\end{aligned}
2
2
⋅
5
17
⋅
34
=
2
⋅
2
⋅
5
⋅
17
⋅
2
⋅
17
=
2
⋅
5
⋅
2
⋅
17
⋅
2
⋅
17
=
10
⋅
(
2
⋅
2
)
⋅
(
17
⋅
17
)
=
10
⋅
2
⋅
17
=
340
Ответ:
340
340
340
.
