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Найдите значение выражения
21
⋅
24
14
\dfrac{\sqrt{21}\cdot \sqrt{24}}{\sqrt{14}}
14
21
⋅
24
Ответ:
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Решение
21
⋅
24
14
=
3
⋅
7
⋅
8
⋅
3
2
⋅
7
=
3
⋅
7
⋅
2
⋅
2
⋅
3
2
⋅
7
=
2
⋅
2
⋅
(
3
⋅
3
)
⋅
7
2
⋅
7
=
2
⋅
3
⋅
2
⋅
7
2
⋅
7
=
6
\begin{aligned}
{}& \dfrac{\sqrt{21}\cdot \sqrt{24}}{\sqrt{14}} = \dfrac{\sqrt{3\cdot 7}\cdot\sqrt{8\cdot 3}}{\sqrt{2\cdot 7}} = \\
& \dfrac{\sqrt{3}\cdot \sqrt{7}\cdot 2\cdot \sqrt{2}\cdot \sqrt{3}}{\sqrt{2}\cdot \sqrt{7}} = \\
& \dfrac{2\cdot \sqrt{2}\cdot (\sqrt{3}\cdot\sqrt{3})\cdot \sqrt{7}}{\sqrt{2}\cdot \sqrt{7}} = \\
& \dfrac{2\cdot 3\cdot \sqrt{2}\cdot \sqrt{7}}{\sqrt{2}\cdot \sqrt{7}} = \\
& 6
\end{aligned}
14
21
⋅
24
=
2
⋅
7
3
⋅
7
⋅
8
⋅
3
=
2
⋅
7
3
⋅
7
⋅
2
⋅
2
⋅
3
=
2
⋅
7
2
⋅
2
⋅
(
3
⋅
3
)
⋅
7
=
2
⋅
7
2
⋅
3
⋅
2
⋅
7
=
6
Ответ:
6
6
6
.
