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Найдите значение выражения
78
⋅
147
26
\dfrac{\sqrt{78}\cdot \sqrt{147}}{\sqrt{26}}
26
78
⋅
147
Ответ:
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Решение
78
⋅
147
26
=
2
⋅
3
⋅
13
⋅
3
⋅
49
2
⋅
13
=
2
⋅
3
⋅
13
⋅
7
⋅
3
2
⋅
13
=
7
⋅
2
⋅
(
3
⋅
3
)
⋅
13
2
⋅
13
=
7
⋅
3
⋅
2
⋅
13
2
⋅
13
=
21
\begin{aligned}
{}& \dfrac{\sqrt{78}\cdot \sqrt{147}}{\sqrt{26}} = \dfrac{\sqrt{2\cdot 3\cdot 13}\cdot\sqrt{3\cdot 49}}{\sqrt{2\cdot 13}} = \\
& \dfrac{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{13}\cdot 7\cdot \sqrt{3}}{\sqrt{2}\cdot \sqrt{13}} = \\
& \dfrac{7\cdot \sqrt{2}\cdot (\sqrt{3}\cdot\sqrt{3})\cdot \sqrt{13}}{\sqrt{2}\cdot \sqrt{13}} = \\
& \dfrac{7\cdot 3\cdot \sqrt{2}\cdot \sqrt{13}}{\sqrt{2}\cdot \sqrt{13}} = \\
& 21
\end{aligned}
26
78
⋅
147
=
2
⋅
13
2
⋅
3
⋅
13
⋅
3
⋅
49
=
2
⋅
13
2
⋅
3
⋅
13
⋅
7
⋅
3
=
2
⋅
13
7
⋅
2
⋅
(
3
⋅
3
)
⋅
13
=
2
⋅
13
7
⋅
3
⋅
2
⋅
13
=
21
Ответ:
21
21
21
.
