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Найдите значение выражения
6
3
⋅
3
13
⋅
39
6\sqrt{3}\cdot 3\sqrt{13}\cdot \sqrt{39}
6
3
⋅
3
13
⋅
39
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Решение
6
3
⋅
3
13
⋅
39
=
6
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
6
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
18
⋅
(
3
⋅
3
)
⋅
(
13
⋅
13
)
=
18
⋅
3
⋅
13
=
702
\begin{aligned}
{}& 6\sqrt{3}\cdot 3\sqrt{13}\cdot \sqrt{39} = 6\cdot \sqrt{3}\cdot 3\cdot \sqrt{13}\cdot \sqrt{3\cdot 13} = \\
& 6\cdot 3\cdot \sqrt{3}\cdot \sqrt{13}\cdot \sqrt{3}\cdot \sqrt{13} = \\
& 18\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{13}\cdot\sqrt{13}) = \\
& 18\cdot 3\cdot 13 = 702
\end{aligned}
6
3
⋅
3
13
⋅
39
=
6
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
6
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
18
⋅
(
3
⋅
3
)
⋅
(
13
⋅
13
)
=
18
⋅
3
⋅
13
=
702
Ответ:
702
702
702
.
