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Найдите значение выражения
5
3
⋅
6
7
⋅
21
5\sqrt{3}\cdot 6\sqrt{7}\cdot \sqrt{21}
5
3
⋅
6
7
⋅
21
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Решение
5
3
⋅
6
7
⋅
21
=
5
⋅
3
⋅
6
⋅
7
⋅
3
⋅
7
=
5
⋅
6
⋅
3
⋅
7
⋅
3
⋅
7
=
30
⋅
(
3
⋅
3
)
⋅
(
7
⋅
7
)
=
30
⋅
3
⋅
7
=
630
\begin{aligned}
{}& 5\sqrt{3}\cdot 6\sqrt{7}\cdot \sqrt{21} = 5\cdot \sqrt{3}\cdot 6\cdot \sqrt{7}\cdot \sqrt{3\cdot 7} = \\
& 5\cdot 6\cdot \sqrt{3}\cdot \sqrt{7}\cdot \sqrt{3}\cdot \sqrt{7} = \\
& 30\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 30\cdot 3\cdot 7 = 630
\end{aligned}
5
3
⋅
6
7
⋅
21
=
5
⋅
3
⋅
6
⋅
7
⋅
3
⋅
7
=
5
⋅
6
⋅
3
⋅
7
⋅
3
⋅
7
=
30
⋅
(
3
⋅
3
)
⋅
(
7
⋅
7
)
=
30
⋅
3
⋅
7
=
630
Ответ:
630
630
630
.
