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6654b35e
Найдите значение выражения
51
⋅
68
12
\dfrac{\sqrt{51}\cdot \sqrt{68}}{\sqrt{12}}
12
51
⋅
68
Ответ:
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Решение
51
⋅
68
12
=
3
⋅
17
⋅
4
⋅
17
4
⋅
3
=
3
⋅
17
⋅
2
⋅
17
2
⋅
3
=
2
⋅
3
⋅
(
17
⋅
17
)
2
⋅
3
=
2
⋅
17
⋅
3
2
⋅
3
=
17
\begin{aligned}
{}& \dfrac{\sqrt{51}\cdot \sqrt{68}}{\sqrt{12}} = \dfrac{\sqrt{3\cdot 17}\cdot\sqrt{4\cdot 17}}{\sqrt{4\cdot 3}} = \\
& \dfrac{\sqrt{3}\cdot \sqrt{17}\cdot 2\cdot \sqrt{17}}{2\cdot \sqrt{3}} = \\
& \dfrac{2\cdot \sqrt{3}\cdot (\sqrt{17}\cdot\sqrt{17})}{2\cdot \sqrt{3}} = \\
& \dfrac{2\cdot 17\cdot \sqrt{3}}{2\cdot \sqrt{3}} = 17
\end{aligned}
12
51
⋅
68
=
4
⋅
3
3
⋅
17
⋅
4
⋅
17
=
2
⋅
3
3
⋅
17
⋅
2
⋅
17
=
2
⋅
3
2
⋅
3
⋅
(
17
⋅
17
)
=
2
⋅
3
2
⋅
17
⋅
3
=
17
Ответ:
17
17
17
.
