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Найдите значение выражения
48
⋅
156
52
\dfrac{\sqrt{48}\cdot \sqrt{156}}{\sqrt{52}}
52
48
⋅
156
Ответ:
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Решение
48
⋅
156
52
=
16
⋅
3
⋅
4
⋅
3
⋅
13
4
⋅
13
=
4
⋅
3
⋅
2
⋅
3
⋅
13
2
⋅
13
=
8
⋅
(
3
⋅
3
)
⋅
13
2
⋅
13
=
8
⋅
3
⋅
13
2
⋅
13
=
12
\begin{aligned}
{}& \dfrac{\sqrt{48}\cdot \sqrt{156}}{\sqrt{52}} = \dfrac{\sqrt{16\cdot 3}\cdot\sqrt{4\cdot 3\cdot 13}}{\sqrt{4\cdot 13}} = \\
& \dfrac{4\cdot \sqrt{3}\cdot 2\cdot \sqrt{3}\cdot \sqrt{13}}{2\cdot \sqrt{13}} = \\
& \dfrac{8\cdot (\sqrt{3}\cdot\sqrt{3})\cdot \sqrt{13}}{2\cdot \sqrt{13}} = \\
& \dfrac{8\cdot 3\cdot \sqrt{13}}{2\cdot \sqrt{13}} = 12
\end{aligned}
52
48
⋅
156
=
4
⋅
13
16
⋅
3
⋅
4
⋅
3
⋅
13
=
2
⋅
13
4
⋅
3
⋅
2
⋅
3
⋅
13
=
2
⋅
13
8
⋅
(
3
⋅
3
)
⋅
13
=
2
⋅
13
8
⋅
3
⋅
13
=
12
Ответ:
12
12
12
.
