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病例1 求(-2)2~(1/2)的值．解:(-2)2~(1/2)=-2．病因:概念理解错误．病理:(-2)2~(1/2)表示(-2)2的算术平方根,即4的算术平方根,是非负数．正解:(-2)2~(1/2)=4~(1/2)=2．病例2 求(36)~(1/2)的值是( )． A．6 B．-6 C．±6 D．6~(1/2) 评:因(±6)2=36,所以(36)~(1/2)=±6,故选C．病因:概念理解错误．病理:本题把平方根与算术平方根的概念混淆了,(36)~(1/2)表示 36的算术平方根,任何非负数的算术平方根都只能是非负数．正解:因(36)~(1/2)=6,故选A．
Case 1 Find the value of (-2) 2~(1/2). Solution: (-2) 2~(1/2)=-2. Etiology: concept understanding error. Pathology: (-2) 2~(1/2) denotes the square root of the (-2)2 arithmetic, that is, the arithmetic square root of 4. It is a non-negative number. Positive solution: (-2) 2~(1/2)=4~(1/2)=2. In case 2, the value of (36) ~ (1/2) is (). A. 6 B. -6 C. ±6 D. 6~(1/2) Comment: Because (±6)2=36, so (36)~(1/2)=±6, so choose C. Etiology: concept understanding error. Pathology: This question confuses the concept of square root with the square root of arithmetic. (36) ~ (1/2) denotes the square root of the arithmetic 36. Any non-negative arithmetic square root can only be non-negative. Positive solution: Because (36) ~ (1/2) = 6, so choose A.