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Найдите значение выражения
42
⋅
108
14
\dfrac{\sqrt{42}\cdot \sqrt{108}}{\sqrt{14}}
14
42
⋅
108
Ответ:
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Решение
42
⋅
108
14
=
2
⋅
3
⋅
7
⋅
4
⋅
27
2
⋅
7
=
2
⋅
3
⋅
7
⋅
6
⋅
3
2
⋅
7
=
6
⋅
2
⋅
(
3
⋅
3
)
⋅
7
2
⋅
7
=
6
⋅
3
⋅
2
⋅
7
2
⋅
7
=
18
\begin{aligned}
{}& \dfrac{\sqrt{42}\cdot \sqrt{108}}{\sqrt{14}} = \dfrac{\sqrt{2\cdot 3\cdot 7}\cdot\sqrt{4\cdot 27}}{\sqrt{2\cdot 7}} = \\
& \dfrac{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{7}\cdot 6\cdot \sqrt{3}}{\sqrt{2}\cdot \sqrt{7}} = \\
& \dfrac{6\cdot \sqrt{2}\cdot (\sqrt{3}\cdot\sqrt{3})\cdot \sqrt{7}}{\sqrt{2}\cdot \sqrt{7}} = \\
& \dfrac{6\cdot 3\cdot \sqrt{2}\cdot \sqrt{7}}{\sqrt{2}\cdot \sqrt{7}} = \\
& 18
\end{aligned}
14
42
⋅
108
=
2
⋅
7
2
⋅
3
⋅
7
⋅
4
⋅
27
=
2
⋅
7
2
⋅
3
⋅
7
⋅
6
⋅
3
=
2
⋅
7
6
⋅
2
⋅
(
3
⋅
3
)
⋅
7
=
2
⋅
7
6
⋅
3
⋅
2
⋅
7
=
18
Ответ:
18
18
18
.
