Square root, also called quadratic square root, is expressed as √ ~ The square root that belongs to non-negative number is called arithmetic square root, which is a kind of square root. A positive number has two real square roots, which are in opposite directions. Negative numbers have no square root in the real number range, and the square root of 0 is 0.
The greater the root sign, the greater the corresponding arithmetic square root (true for all positive numbers). If a positive number has a square root, then there must be two, and it is reciprocal. Obviously, if we know one of these two square roots, we can get the other square root in time according to the concept of reciprocal.
Each transition number is changed by the last transition number, and then the single digits of the last transition number are multiplied by 20. If carry is required, advance 1, and then increase the unit number by ten digits. And so on, each bit adds a new operand. Simply put, the transition number 27 is 1 of the first quotient multiplied by 20, and 0 in the unit is replaced by 7 in the second quotient.
The transition number 343 is 17 of the first two quotients multiplied by 20=340, where the 0th bit is replaced by 3 of the third quotients, the third transition number 3462 is 173 of the first three quotients multiplied by 20=3460, and the 0th bit is replaced by 2 of the fourth quotients, and so on.
Analysis of Teaching Emphasis and Difficulties
1, this section focuses on the concepts of square root and arithmetic square root. Square root is the basis of radical operation and the preparatory knowledge for introducing irrational numbers. The correct understanding of the concept of square root is helpful to the understanding of symbolic representation, and it is the premise of correct square root operation, which directly affects the learning of quadratic roots. The teaching of arithmetic roots is not only the focus of this chapter, but also the focus of mathematics learning in the future.
2. The difficulty of this section is the difference and connection between square root and arithmetic square root. First of all, these two concepts are easily confused, and it is not easy for students to distinguish the meanings of their respective symbols. In teaching, we should grasp the square root of arithmetic square root, make clear the meaning of each symbol, and distinguish the difference between the two representations.