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Найдите значение выражения
18
⋅
192
24
\dfrac{\sqrt{18}\cdot \sqrt{192}}{\sqrt{24}}
24
18
⋅
192
Ответ:
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Решение
18
⋅
192
24
=
2
⋅
9
⋅
64
⋅
3
8
⋅
3
=
3
⋅
2
⋅
8
⋅
3
2
⋅
2
⋅
3
=
24
⋅
2
⋅
3
2
⋅
2
⋅
3
=
12
\begin{aligned}
{}& \dfrac{\sqrt{18}\cdot \sqrt{192}}{\sqrt{24}} = \dfrac{\sqrt{2\cdot 9}\cdot\sqrt{64\cdot 3}}{\sqrt{8\cdot 3}} = \\
& \dfrac{3\cdot \sqrt{2}\cdot 8\cdot \sqrt{3}}{2\cdot \sqrt{2}\cdot \sqrt{3}} = \\
& \dfrac{24\cdot \sqrt{2}\cdot \sqrt{3}}{2\cdot \sqrt{2}\cdot \sqrt{3}} = \\
& 12
\end{aligned}
24
18
⋅
192
=
8
⋅
3
2
⋅
9
⋅
64
⋅
3
=
2
⋅
2
⋅
3
3
⋅
2
⋅
8
⋅
3
=
2
⋅
2
⋅
3
24
⋅
2
⋅
3
=
12
Ответ:
12
12
12
.
