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Найдите значение выражения
8
⋅
27
54
\dfrac{\sqrt{8}\cdot \sqrt{27}}{\sqrt{54}}
54
8
⋅
27
Ответ:
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Решение
8
⋅
27
54
=
2
3
⋅
3
3
2
⋅
27
=
2
⋅
2
⋅
3
⋅
3
3
⋅
2
⋅
3
=
6
⋅
2
⋅
3
3
⋅
2
⋅
3
=
2
\begin{aligned}
{}& \dfrac{\sqrt{8}\cdot \sqrt{27}}{\sqrt{54}} = \dfrac{\sqrt{2^{3}}\cdot\sqrt{3^{3}}}{\sqrt{2\cdot 27}} = \\
& \dfrac{2\cdot \sqrt{2}\cdot 3\cdot \sqrt{3}}{3\cdot \sqrt{2}\cdot \sqrt{3}} = \\
& \dfrac{6\cdot \sqrt{2}\cdot \sqrt{3}}{3\cdot \sqrt{2}\cdot \sqrt{3}} = \\
& 2
\end{aligned}
54
8
⋅
27
=
2
⋅
27
2
3
⋅
3
3
=
3
⋅
2
⋅
3
2
⋅
2
⋅
3
⋅
3
=
3
⋅
2
⋅
3
6
⋅
2
⋅
3
=
2
Ответ:
2
2
2
.
