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Найдите значение выражения
72
⋅
147
54
\dfrac{\sqrt{72}\cdot \sqrt{147}}{\sqrt{54}}
54
72
⋅
147
Ответ:
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Решение
72
⋅
147
54
=
8
⋅
9
⋅
3
⋅
49
2
⋅
27
=
6
⋅
2
⋅
7
⋅
3
3
⋅
2
⋅
3
=
42
⋅
2
⋅
3
3
⋅
2
⋅
3
=
14
\begin{aligned}
{}& \dfrac{\sqrt{72}\cdot \sqrt{147}}{\sqrt{54}} = \dfrac{\sqrt{8\cdot 9}\cdot\sqrt{3\cdot 49}}{\sqrt{2\cdot 27}} = \\
& \dfrac{6\cdot \sqrt{2}\cdot 7\cdot \sqrt{3}}{3\cdot \sqrt{2}\cdot \sqrt{3}} = \\
& \dfrac{42\cdot \sqrt{2}\cdot \sqrt{3}}{3\cdot \sqrt{2}\cdot \sqrt{3}} = \\
& 14
\end{aligned}
54
72
⋅
147
=
2
⋅
27
8
⋅
9
⋅
3
⋅
49
=
3
⋅
2
⋅
3
6
⋅
2
⋅
7
⋅
3
=
3
⋅
2
⋅
3
42
⋅
2
⋅
3
=
14
Ответ:
14
14
14
.
