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Найдите значение выражения
18
⋅
108
54
\dfrac{\sqrt{18}\cdot \sqrt{108}}{\sqrt{54}}
54
18
⋅
108
Ответ:
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Решение
18
⋅
108
54
=
2
⋅
9
⋅
4
⋅
27
2
⋅
27
=
3
⋅
2
⋅
6
⋅
3
3
⋅
2
⋅
3
=
18
⋅
2
⋅
3
3
⋅
2
⋅
3
=
6
\begin{aligned}
{}& \dfrac{\sqrt{18}\cdot \sqrt{108}}{\sqrt{54}} = \dfrac{\sqrt{2\cdot 9}\cdot\sqrt{4\cdot 27}}{\sqrt{2\cdot 27}} = \\
& \dfrac{3\cdot \sqrt{2}\cdot 6\cdot \sqrt{3}}{3\cdot \sqrt{2}\cdot \sqrt{3}} = \\
& \dfrac{18\cdot \sqrt{2}\cdot \sqrt{3}}{3\cdot \sqrt{2}\cdot \sqrt{3}} = \\
& 6
\end{aligned}
54
18
⋅
108
=
2
⋅
27
2
⋅
9
⋅
4
⋅
27
=
3
⋅
2
⋅
3
3
⋅
2
⋅
6
⋅
3
=
3
⋅
2
⋅
3
18
⋅
2
⋅
3
=
6
Ответ:
6
6
6
.
