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Найдите значение выражения
2
3
⋅
6
7
⋅
21
2\sqrt{3}\cdot 6\sqrt{7}\cdot \sqrt{21}
2
3
⋅
6
7
⋅
21
Ответ:
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Решение
2
3
⋅
6
7
⋅
21
=
2
⋅
3
⋅
6
⋅
7
⋅
3
⋅
7
=
2
⋅
6
⋅
3
⋅
7
⋅
3
⋅
7
=
12
⋅
(
3
⋅
3
)
⋅
(
7
⋅
7
)
=
12
⋅
3
⋅
7
=
252
\begin{aligned}
{}& 2\sqrt{3}\cdot 6\sqrt{7}\cdot \sqrt{21} = 2\cdot \sqrt{3}\cdot 6\cdot \sqrt{7}\cdot \sqrt{3\cdot 7} = \\
& 2\cdot 6\cdot \sqrt{3}\cdot \sqrt{7}\cdot \sqrt{3}\cdot \sqrt{7} = \\
& 12\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 12\cdot 3\cdot 7 = 252
\end{aligned}
2
3
⋅
6
7
⋅
21
=
2
⋅
3
⋅
6
⋅
7
⋅
3
⋅
7
=
2
⋅
6
⋅
3
⋅
7
⋅
3
⋅
7
=
12
⋅
(
3
⋅
3
)
⋅
(
7
⋅
7
)
=
12
⋅
3
⋅
7
=
252
Ответ:
252
252
252
.
