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Найдите значение выражения
18
⋅
24
⋅
48
\sqrt{18}\cdot \sqrt{24}\cdot \sqrt{48}
18
⋅
24
⋅
48
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Решение
18
⋅
24
⋅
48
=
2
⋅
9
⋅
8
⋅
3
⋅
16
⋅
3
=
3
⋅
2
⋅
2
⋅
2
⋅
3
⋅
4
⋅
3
=
24
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
24
⋅
2
⋅
3
=
144
\begin{aligned}
{}& \sqrt{18}\cdot \sqrt{24}\cdot \sqrt{48} = \sqrt{2\cdot 9}\cdot \sqrt{8\cdot 3}\cdot \sqrt{16\cdot 3} = \\
& 3\cdot \sqrt{2}\cdot 2\cdot \sqrt{2}\cdot \sqrt{3}\cdot 4\cdot \sqrt{3} = \\
& 24\cdot (\sqrt{2}\cdot\sqrt{2})\cdot (\sqrt{3}\cdot\sqrt{3}) = \\
& 24\cdot 2\cdot 3 = 144
\end{aligned}
18
⋅
24
⋅
48
=
2
⋅
9
⋅
8
⋅
3
⋅
16
⋅
3
=
3
⋅
2
⋅
2
⋅
2
⋅
3
⋅
4
⋅
3
=
24
⋅
(
2
⋅
2
)
⋅
(
3
⋅
3
)
=
24
⋅
2
⋅
3
=
144
Ответ:
144
144
144
.
