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61371c0a
Найдите значение выражения
6
⋅
51
34
\dfrac{\sqrt{6}\cdot \sqrt{51}}{\sqrt{34}}
34
6
⋅
51
Ответ:
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Решение
6
⋅
51
34
=
2
⋅
3
⋅
3
⋅
17
2
⋅
17
=
2
⋅
3
⋅
3
⋅
17
2
⋅
17
=
2
⋅
(
3
⋅
3
)
⋅
17
2
⋅
17
=
3
⋅
2
⋅
17
2
⋅
17
=
3
\begin{aligned}
{}& \dfrac{\sqrt{6}\cdot \sqrt{51}}{\sqrt{34}} = \dfrac{\sqrt{2\cdot 3}\cdot\sqrt{3\cdot 17}}{\sqrt{2\cdot 17}} = \\
& \dfrac{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{3}\cdot \sqrt{17}}{\sqrt{2}\cdot \sqrt{17}} = \\
& \dfrac{\sqrt{2}\cdot (\sqrt{3}\cdot\sqrt{3})\cdot \sqrt{17}}{\sqrt{2}\cdot \sqrt{17}} = \\
& \dfrac{3\cdot \sqrt{2}\cdot \sqrt{17}}{\sqrt{2}\cdot \sqrt{17}} = \\
& 3
\end{aligned}
34
6
⋅
51
=
2
⋅
17
2
⋅
3
⋅
3
⋅
17
=
2
⋅
17
2
⋅
3
⋅
3
⋅
17
=
2
⋅
17
2
⋅
(
3
⋅
3
)
⋅
17
=
2
⋅
17
3
⋅
2
⋅
17
=
3
Ответ:
3
3
3
.
