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Найдите значение выражения
11
⋅
33
⋅
27
\sqrt{11}\cdot \sqrt{33}\cdot \sqrt{27}
11
⋅
33
⋅
27
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Решение
11
⋅
33
⋅
27
=
11
⋅
3
⋅
11
⋅
3
3
=
11
⋅
3
⋅
11
⋅
3
⋅
3
=
3
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
3
⋅
3
⋅
11
=
99
\begin{aligned}
{}& \sqrt{11}\cdot \sqrt{33}\cdot \sqrt{27} = \sqrt{11}\cdot \sqrt{3\cdot 11}\cdot \sqrt{3^{3}} = \\
& \sqrt{11}\cdot \sqrt{3}\cdot \sqrt{11}\cdot 3\cdot \sqrt{3} = \\
& 3\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{11}\cdot\sqrt{11}) = \\
& 3\cdot 3\cdot 11 = 99
\end{aligned}
11
⋅
33
⋅
27
=
11
⋅
3
⋅
11
⋅
3
3
=
11
⋅
3
⋅
11
⋅
3
⋅
3
=
3
⋅
(
3
⋅
3
)
⋅
(
11
⋅
11
)
=
3
⋅
3
⋅
11
=
99
Ответ:
99
99
99
.
