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Найдите значение выражения
4
3
⋅
3
13
⋅
39
4\sqrt{3}\cdot 3\sqrt{13}\cdot \sqrt{39}
4
3
⋅
3
13
⋅
39
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Решение
4
3
⋅
3
13
⋅
39
=
4
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
4
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
12
⋅
(
3
⋅
3
)
⋅
(
13
⋅
13
)
=
12
⋅
3
⋅
13
=
468
\begin{aligned}
{}& 4\sqrt{3}\cdot 3\sqrt{13}\cdot \sqrt{39} = 4\cdot \sqrt{3}\cdot 3\cdot \sqrt{13}\cdot \sqrt{3\cdot 13} = \\
& 4\cdot 3\cdot \sqrt{3}\cdot \sqrt{13}\cdot \sqrt{3}\cdot \sqrt{13} = \\
& 12\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{13}\cdot\sqrt{13}) = \\
& 12\cdot 3\cdot 13 = 468
\end{aligned}
4
3
⋅
3
13
⋅
39
=
4
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
4
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
12
⋅
(
3
⋅
3
)
⋅
(
13
⋅
13
)
=
12
⋅
3
⋅
13
=
468
Ответ:
468
468
468
.
