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√(a×b)=√a×√b成立的條件是a>=0或b>=0

Floor 3 巨大八爪鱼 7/13/25 2:06

√(-a)=i√a僅當a>=0時成立。

當a=1時,√(-a)=i,i√a=i。

當a=-1時,√(-a)=1,i√a=i×i=-1,兩者不相等。


所以,用√(a²b)=a√b的方法化簡二次根式時,必須保證a²>=0。當a²<0時,a²必須留在根號內,不能提出來!!!!!

巨大八爪鱼 7/13/25 11:12
嚴格地說應該是√(a²b)=|a|√b。

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