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根式运算概念性很强,概念混淆、模糊常引起解题的失误。特别是算术根概念不清引起的错误最为突出。其原因是在实数范围内讨论根式,要求对实数施行开方运算后还能得到实数,必须把偶次方根的被开方数约束在非负数的范围内,而对奇次方根则不需要这个限制。根式运算的有关问题往往又和分式、因式分解、方程、函数、指数、对数紧密联系在一起,因此它是中学代数中的重要内容之一。在审题时既要将各部分联系起来分析,而又要在联系的角度上去仔细观察每一部分,做到由局部到整体,再从整体到局部,这样才容易找到解题
The concept of root-based computing is very strong. Concept confusion and ambiguity often cause mistakes in solving problems. In particular, the errors caused by the unclear concept of the arithmetic root are the most prominent. The reason for this is that the discussion of the root formula in the real number range requires real numbers to be obtained after the real number is applied to the real number. The number of square roots to be raised must be confined to the range of non-negative numbers, but not to the odd roots. Need this limit. The problems associated with root-based operations are often tied to fractional, factorized, equations, functions, exponentials, and logarithms, so it is one of the most important aspects of algebra in middle schools. When examining the issue, we must analyze and analyze each part, and we must carefully observe each part from the point of view of contact. From the part to the whole, and then from the whole to the part, it is easy to find the solution.