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Найдите значение выражения
88
⋅
187
34
\dfrac{\sqrt{88}\cdot \sqrt{187}}{\sqrt{34}}
34
88
⋅
187
Ответ:
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Решение
88
⋅
187
34
=
8
⋅
11
⋅
11
⋅
17
2
⋅
17
=
2
⋅
2
⋅
11
⋅
11
⋅
17
2
⋅
17
=
2
⋅
2
⋅
(
11
⋅
11
)
⋅
17
2
⋅
17
=
2
⋅
11
⋅
2
⋅
17
2
⋅
17
=
22
\begin{aligned}
{}& \dfrac{\sqrt{88}\cdot \sqrt{187}}{\sqrt{34}} = \dfrac{\sqrt{8\cdot 11}\cdot\sqrt{11\cdot 17}}{\sqrt{2\cdot 17}} = \\
& \dfrac{2\cdot \sqrt{2}\cdot \sqrt{11}\cdot \sqrt{11}\cdot \sqrt{17}}{\sqrt{2}\cdot \sqrt{17}} = \\
& \dfrac{2\cdot \sqrt{2}\cdot (\sqrt{11}\cdot\sqrt{11})\cdot \sqrt{17}}{\sqrt{2}\cdot \sqrt{17}} = \\
& \dfrac{2\cdot 11\cdot \sqrt{2}\cdot \sqrt{17}}{\sqrt{2}\cdot \sqrt{17}} = \\
& 22
\end{aligned}
34
88
⋅
187
=
2
⋅
17
8
⋅
11
⋅
11
⋅
17
=
2
⋅
17
2
⋅
2
⋅
11
⋅
11
⋅
17
=
2
⋅
17
2
⋅
2
⋅
(
11
⋅
11
)
⋅
17
=
2
⋅
17
2
⋅
11
⋅
2
⋅
17
=
22
Ответ:
22
22
22
.
