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Найдите значение выражения
128
⋅
156
78
\dfrac{\sqrt{128}\cdot \sqrt{156}}{\sqrt{78}}
78
128
⋅
156
Ответ:
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Решение
128
⋅
156
78
=
2
7
⋅
4
⋅
3
⋅
13
2
⋅
3
⋅
13
=
8
⋅
2
⋅
2
⋅
3
⋅
13
2
⋅
3
⋅
13
=
16
⋅
2
⋅
3
⋅
13
2
⋅
3
⋅
13
=
16
\begin{aligned}
{}& \dfrac{\sqrt{128}\cdot \sqrt{156}}{\sqrt{78}} = \dfrac{\sqrt{2^{7}}\cdot\sqrt{4\cdot 3\cdot 13}}{\sqrt{2\cdot 3\cdot 13}} = \\
& \dfrac{8\cdot \sqrt{2}\cdot 2\cdot \sqrt{3}\cdot \sqrt{13}}{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{13}} = \\
& \dfrac{16\cdot \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{13}}{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{13}} = \\
& 16
\end{aligned}
78
128
⋅
156
=
2
⋅
3
⋅
13
2
7
⋅
4
⋅
3
⋅
13
=
2
⋅
3
⋅
13
8
⋅
2
⋅
2
⋅
3
⋅
13
=
2
⋅
3
⋅
13
16
⋅
2
⋅
3
⋅
13
=
16
Ответ:
16
16
16
.
