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WaySolo
@WaySolo
August 2021
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[tex] \sqrt{} \sqrt{3} \sqrt[3]{9} [/tex]÷[tex] \sqrt[4]{27} [/tex]
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sangers1959
Verified answer
=(3^(1/2)*9^(1/6)^(1/2)/27^(1/4)=(3^(1/2)*3^(1/3))^(1/2)/27^(1/4)=
=(3^(5/6))^(1/2)/3^(3/4)=3^(5/12)/3^(3/4)=3^(5/12-3/4)=3^(-1/3)=1/∛3.
∛9=3^(2/3)
√((3^1/2)*3(2/3))=√(3^(1/2+2/3))=√(3^(5/6))=3^(5/6)^(1/2)=3^(5/12)
27^(1/4)=3^(3/4)
3^(5/12)/3^(3/4)=3^(5/12-3/4)=3^(-1/3)=1/∛3.
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WaySolo
вынос мозга переписала и переришала по вашему образцу, но отчет получился другой
WaySolo
ответ*
sangers1959
Сейчас попробую решить другим методом.
sangers1959
Нет, всё верно.
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Answers & Comments
Verified answer
=(3^(1/2)*9^(1/6)^(1/2)/27^(1/4)=(3^(1/2)*3^(1/3))^(1/2)/27^(1/4)==(3^(5/6))^(1/2)/3^(3/4)=3^(5/12)/3^(3/4)=3^(5/12-3/4)=3^(-1/3)=1/∛3.
∛9=3^(2/3)
√((3^1/2)*3(2/3))=√(3^(1/2+2/3))=√(3^(5/6))=3^(5/6)^(1/2)=3^(5/12)
27^(1/4)=3^(3/4)
3^(5/12)/3^(3/4)=3^(5/12-3/4)=3^(-1/3)=1/∛3.