The difference between square root and arithmetic square root 1, the definition of square root: if x? =a, then x is the square root of a,
If 2? =4, 2 is the square root of 4, (-2)? =4, -2 is the square root of 4,
Definition of arithmetic square root: the positive square root of a non-negative number is called its arithmetic square.
For example, 2 and -2 are the square root of 4, and 2 is the arithmetic square root of 4.
2. Heterogeneous number: a positive number has two square roots, the two square roots are in opposite directions, and there is only one arithmetic square root of a positive number.
3. Different representations: the square root of the former non-negative number A is the positive and negative square root of A, and the arithmetic square root of the latter non-negative number A is the positive square root of A. ..
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The existence condition of (1) is the same: the square root and arithmetic square root are only non-negative,
(2) Inclusion relation: the square root contains the arithmetic square root, and the arithmetic square root is the non-negative square root of the square root.
(3) The square root and arithmetic square root of 0 are both 0.
note:
1, a positive number has two square roots, the two square roots are in opposite directions, a negative number has no square root, and the square root of 0 is 0.
2. There is only one arithmetic square root of non-negative numbers.
Square root and square root
square root
If the square of a number is equal to A, then this number is called the square root of A (square root is also called quadratic root).
extract a root
The operation of finding the square root of a number is called square root, and A is called the root sign.
main points
The definition of 1. square root is expressed in mathematical language: if x? =a, then x is called the square root of a.
2. Three properties of square root:
(1) A positive number A has two square roots, which are reciprocal;
(2) The square root of 0 is 0;
(3) Negative numbers have no square root.
3. Square sum and square root are reciprocal operations. Square a positive number, and its way of thinking is opposite to power. If you find the square root of 9, you can think like this: What number is equal to 9 in square? Because of 3? =9,(-3)? =9, so the square roots of 9 are 3 and -3.
Expanding reading: how to learn junior high school mathematics well 1. Explore concepts and formulas carefully.
Many students pay insufficient attention to concepts and formulas. This problem is reflected in three aspects: first, the understanding of the concept only stays on the surface of the text, and the special situation of the concept is not paid enough attention. For example, in the concept of algebraic expression (an expression expressed by letters or numbers is algebraic expression), many students ignore that "a single letter or number is also algebraic expression". Second, concepts and formulas are blindly memorized and have nothing to do with practical topics. The knowledge learned in this way can't be well connected with solving problems. Third, some students do not pay attention to the memory of mathematical concepts and formulas. Memory is the basis of understanding. If you can't memorize concepts and formulas, how can you skillfully use them in the topic?
Concept is the cornerstone of mathematics. For every definition, theorem and formula rule, remember what you understand and what you don't understand for the time being, and apply it to solving problems on the basis of memory to deepen your understanding. On the basis of keeping in mind its content, we know how it came from and where it is used. Connect concepts and formulas with problem solving, and understand how they are applied to the topic, so as to concretize the concepts learned in your mind, deepen your understanding of knowledge and realize flexible learning and application.
2. Look at the examples and do exercises, and learn to summarize the questions and methods.
1) How to look at examples and do exercises? If you want to learn math well, you must read more examples and do more exercises. We look at examples and do exercises in order to understand the application of definitions, theorems and formulas, which is the idea and method of learning mathematics. Each question is aimed at one or several knowledge points, which will reflect a certain way of thinking, that is, the way of thinking to solve problems. Every time you read or do a problem, you should know how to apply mathematical knowledge, clarify its thinking and master its thinking method. After a long time, the "all-purpose" solution of each question type was formed in my mind, that is, the correct mentality. It will be easy to solve this kind of problem at this time. Some students and teachers can do the questions they have talked about, while others can't. They just talk about the matter and stare at some small changes in the problem, and they can't start. The reason is that I don't know how to apply mathematical knowledge and how to think when solving problems.
2) Learn to summarize. The sea of questions is boundless and can never be finished. The topics of mathematics are infinite, but the ideas and methods of mathematics are limited. There are fewer and fewer topics to do, so we must learn to sum up.
Summarize the exercises you have done, reproduce the process of thinking activities, and analyze the sources of ideas and mistakes. It is required to describe one's experiences and feelings in colloquial language, and write whatever comes to mind, so as to dig out general mathematical thinking methods and mathematical thinking methods. What exercises did you do? What concepts, theorems or formulas are used? What problem-solving methods are used? What type does it belong to? What can I skillfully solve and what are the difficulties? Do less or don't do what you can do in the future, do more what you can't do if you have difficulties, and concentrate.
When you can summarize the topics, classify the topics you have done, know which types of questions you can do, master the common methods of solving problems, and which types of questions you can't do, you will really master the tricks of this subject and truly "let it change, I will never move."