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统编《代数》第三册,通过分数指数,求解 n 次根式运算问题,学生困难很大。困难来自于教材159页的规定:“在本章内根式的字母所取的值凡不作特殊说明都必须使被开方式取正值。”为突破这一关,必须注意以下几点:(1)组织讨论:对于第28页例2_1化简(4a~2b~3)~(1/2)(a>3),化简(x~4+x~2y~2)~(1/2)(x>0);第30页例1:计算((25x~4)/(81y~2))~(1/2)(y>0)等题,可让学生在明确算术根概念的基础上,充分认识条件的作用。然后讨论如果没有这些条件,如何化简?并可用第32页第三题:“(a/b)~(1/2)=1/b(ab)~(1/2)
The third series of “Algebra”, through the fractional index, solving n times root problems, students have great difficulties. The difficulty stems from the provision on page 159 of the textbook: “The values of the rooted letters in this chapter must be rounded up to the proper values without any special explanation.” In order to break this line, the following points must be observed: (1) Organization Discussion: For the simplification (2 a ~ 2 b ~ 3) ~ (1/2) (a> 3) of Example 2_1 on page 28 and the simplification (x ~ 4 + x ~ 2y ~ 2) ~ Example 1: Calculate the questions ((25x ~ 4) / (81y ~ 2)) ~ (1/2) (y> 0) and so on. This allows students to define the concept of an arithmetic root , Fully understand the role of conditions. Then discuss how to streamline them without these conditions and use the third question on page 32: "(a / b) ~ (1/2) = 1 / b (ab)