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Найдите значение выражения
3
⋅
54
⋅
72
\sqrt{3}\cdot \sqrt{54}\cdot \sqrt{72}
3
⋅
54
⋅
72
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Решение
3
⋅
54
⋅
72
=
3
⋅
2
⋅
27
⋅
8
⋅
9
=
3
⋅
3
⋅
2
⋅
3
⋅
6
⋅
2
=
18
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
18
⋅
2
⋅
3
=
108
\begin{aligned}
{}& \sqrt{3}\cdot \sqrt{54}\cdot \sqrt{72} = \sqrt{3}\cdot \sqrt{2\cdot 27}\cdot \sqrt{8\cdot 9} = \\
& \sqrt{3}\cdot 3\cdot \sqrt{2}\cdot \sqrt{3}\cdot 6\cdot \sqrt{2} = \\
& 18\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 18\cdot 2\cdot 3 = 108
\end{aligned}
3
⋅
54
⋅
72
=
3
⋅
2
⋅
27
⋅
8
⋅
9
=
3
⋅
3
⋅
2
⋅
3
⋅
6
⋅
2
=
18
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
18
⋅
2
⋅
3
=
108
Ответ:
108
108
108
.
