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Найдите значение выражения
5
2
⋅
3
17
⋅
34
5\sqrt{2}\cdot 3\sqrt{17}\cdot \sqrt{34}
5
2
⋅
3
17
⋅
34
Ответ:
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Решение
5
2
⋅
3
17
⋅
34
=
5
⋅
2
⋅
3
⋅
17
⋅
2
⋅
17
=
5
⋅
3
⋅
2
⋅
17
⋅
2
⋅
17
=
15
⋅
(
2
⋅
2
)
⋅
(
17
⋅
17
)
=
15
⋅
2
⋅
17
=
510
\begin{aligned}
{}& 5\sqrt{2}\cdot 3\sqrt{17}\cdot \sqrt{34} = 5\cdot \sqrt{2}\cdot 3\cdot \sqrt{17}\cdot \sqrt{2\cdot 17} = \\
& 5\cdot 3\cdot \sqrt{2}\cdot \sqrt{17}\cdot \sqrt{2}\cdot \sqrt{17} = \\
& 15\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{17}\cdot\sqrt{17}) = \\
& 15\cdot 2\cdot 17 = 510
\end{aligned}
5
2
⋅
3
17
⋅
34
=
5
⋅
2
⋅
3
⋅
17
⋅
2
⋅
17
=
5
⋅
3
⋅
2
⋅
17
⋅
2
⋅
17
=
15
⋅
(
2
⋅
2
)
⋅
(
17
⋅
17
)
=
15
⋅
2
⋅
17
=
510
Ответ:
510
510
510
.
