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Найдите значение выражения
24
⋅
135
40
\dfrac{\sqrt{24}\cdot \sqrt{135}}{\sqrt{40}}
40
24
⋅
135
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Решение
24
⋅
135
40
=
8
⋅
3
⋅
27
⋅
5
8
⋅
5
=
2
⋅
2
⋅
3
⋅
3
⋅
3
⋅
5
2
⋅
2
⋅
5
=
6
⋅
2
⋅
(
3
⋅
3
)
⋅
5
2
⋅
2
⋅
5
=
6
⋅
3
⋅
2
⋅
5
2
⋅
2
⋅
5
=
9
\begin{aligned}
{}& \dfrac{\sqrt{24}\cdot \sqrt{135}}{\sqrt{40}} = \dfrac{\sqrt{8\cdot 3}\cdot\sqrt{27\cdot 5}}{\sqrt{8\cdot 5}} = \\
& \dfrac{2\cdot \sqrt{2}\cdot \sqrt{3}\cdot 3\cdot \sqrt{3}\cdot \sqrt{5}}{2\cdot \sqrt{2}\cdot \sqrt{5}} = \\
& \dfrac{6\cdot \sqrt{2}\cdot (\sqrt{3}\cdot\sqrt{3})\cdot \sqrt{5}}{2\cdot \sqrt{2}\cdot \sqrt{5}} = \\
& \dfrac{6\cdot 3\cdot \sqrt{2}\cdot \sqrt{5}}{2\cdot \sqrt{2}\cdot \sqrt{5}} = \\
& 9
\end{aligned}
40
24
⋅
135
=
8
⋅
5
8
⋅
3
⋅
27
⋅
5
=
2
⋅
2
⋅
5
2
⋅
2
⋅
3
⋅
3
⋅
3
⋅
5
=
2
⋅
2
⋅
5
6
⋅
2
⋅
(
3
⋅
3
)
⋅
5
=
2
⋅
2
⋅
5
6
⋅
3
⋅
2
⋅
5
=
9
Ответ:
9
9
9
.
