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Найдите значение выражения
21
⋅
42
⋅
2
\sqrt{21}\cdot \sqrt{42}\cdot \sqrt{2}
21
⋅
42
⋅
2
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Решение
21
⋅
42
⋅
2
=
3
⋅
7
⋅
2
⋅
3
⋅
7
⋅
2
=
3
⋅
7
⋅
2
⋅
3
⋅
7
⋅
2
=
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
7
⋅
7
)
=
2
⋅
3
⋅
7
=
42
\begin{aligned}
{}& \sqrt{21}\cdot \sqrt{42}\cdot \sqrt{2} = \sqrt{3\cdot 7}\cdot \sqrt{2\cdot 3\cdot 7}\cdot \sqrt{2} = \\
& \sqrt{3}\cdot \sqrt{7}\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{7}\cdot \sqrt{2} = \\
& (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 2\cdot 3\cdot 7 = 42
\end{aligned}
21
⋅
42
⋅
2
=
3
⋅
7
⋅
2
⋅
3
⋅
7
⋅
2
=
3
⋅
7
⋅
2
⋅
3
⋅
7
⋅
2
=
(
2
⋅
2
)
⋅
(
3
⋅
3
)
⋅
(
7
⋅
7
)
=
2
⋅
3
⋅
7
=
42
Ответ:
42
42
42
.
