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Найдите значение выражения
3
3
⋅
3
13
⋅
39
3\sqrt{3}\cdot 3\sqrt{13}\cdot \sqrt{39}
3
3
⋅
3
13
⋅
39
Ответ:
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Решение
3
3
⋅
3
13
⋅
39
=
3
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
3
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
9
⋅
(
3
⋅
3
)
⋅
(
13
⋅
13
)
=
9
⋅
3
⋅
13
=
351
\begin{aligned}
{}& 3\sqrt{3}\cdot 3\sqrt{13}\cdot \sqrt{39} = 3\cdot \sqrt{3}\cdot 3\cdot \sqrt{13}\cdot \sqrt{3\cdot 13} = \\
& 3\cdot 3\cdot \sqrt{3}\cdot \sqrt{13}\cdot \sqrt{3}\cdot \sqrt{13} = \\
& 9\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{13}\cdot\sqrt{13}) = \\
& 9\cdot 3\cdot 13 = 351
\end{aligned}
3
3
⋅
3
13
⋅
39
=
3
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
3
⋅
3
⋅
3
⋅
13
⋅
3
⋅
13
=
9
⋅
(
3
⋅
3
)
⋅
(
13
⋅
13
)
=
9
⋅
3
⋅
13
=
351
Ответ:
351
351
351
.
