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Найдите значение выражения
44
⋅
54
66
\dfrac{\sqrt{44}\cdot \sqrt{54}}{\sqrt{66}}
66
44
⋅
54
Ответ:
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Решение
44
⋅
54
66
=
4
⋅
11
⋅
2
⋅
27
2
⋅
3
⋅
11
=
2
⋅
11
⋅
3
⋅
2
⋅
3
2
⋅
3
⋅
11
=
6
⋅
2
⋅
3
⋅
11
2
⋅
3
⋅
11
=
6
\begin{aligned}
{}& \dfrac{\sqrt{44}\cdot \sqrt{54}}{\sqrt{66}} = \dfrac{\sqrt{4\cdot 11}\cdot\sqrt{2\cdot 27}}{\sqrt{2\cdot 3\cdot 11}} = \\
& \dfrac{2\cdot \sqrt{11}\cdot 3\cdot \sqrt{2}\cdot \sqrt{3}}{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{11}} = \\
& \dfrac{6\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{11}}{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{11}} = \\
& 6
\end{aligned}
66
44
⋅
54
=
2
⋅
3
⋅
11
4
⋅
11
⋅
2
⋅
27
=
2
⋅
3
⋅
11
2
⋅
11
⋅
3
⋅
2
⋅
3
=
2
⋅
3
⋅
11
6
⋅
2
⋅
3
⋅
11
=
6
Ответ:
6
6
6
.
