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Найдите значение выражения
129
⋅
147
43
\dfrac{\sqrt{129}\cdot \sqrt{147}}{\sqrt{43}}
43
129
⋅
147
Ответ:
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Решение
129
⋅
147
43
=
3
⋅
43
⋅
3
⋅
49
43
=
3
⋅
43
⋅
7
⋅
3
43
=
7
⋅
(
3
⋅
3
)
⋅
43
43
=
7
⋅
3
⋅
43
43
=
21
\begin{aligned}
{}& \dfrac{\sqrt{129}\cdot \sqrt{147}}{\sqrt{43}} = \dfrac{\sqrt{3\cdot 43}\cdot\sqrt{3\cdot 49}}{\sqrt{43}} = \\
& \dfrac{\sqrt{3}\cdot \sqrt{43}\cdot 7\cdot \sqrt{3}}{\sqrt{43}} = \\
& \dfrac{7\cdot (\sqrt{3}\cdot\sqrt{3})\cdot \sqrt{43}}{\sqrt{43}} = \\
& \dfrac{7\cdot 3\cdot \sqrt{43}}{\sqrt{43}} = 21
\end{aligned}
43
129
⋅
147
=
43
3
⋅
43
⋅
3
⋅
49
=
43
3
⋅
43
⋅
7
⋅
3
=
43
7
⋅
(
3
⋅
3
)
⋅
43
=
43
7
⋅
3
⋅
43
=
21
Ответ:
21
21
21
.
