Many parents have almost forgotten the second radical because they have graduated for many years. Parents who have a good math foundation in junior high school only need to read it a few times now, and the problem-solving methods they learned before will come back.
Then, in the process of simplifying quadratic roots, besides mastering the basic algorithm, what other common simplification skills can solve problems quickly and accurately?
What is the simplest quadratic radical? 1, the factor in the root sign is an integer and the factor is an algebraic expression; 2. The number of square roots does not contain factors or can be opened to the largest factor; 3. The denominator does not contain the root sign.
As long as these three terms in the graph are satisfied, it is the simplest quadratic radical. In layman's terms, the simplest quadratic root is three excluding:
First, the root sign does not contain factors that can be completely opened, second, the denominator does not contain the root sign, and third, the root sign does not contain the denominator.
Skill 1: Simplify by multiplication formula. When polynomials are multiplied, the square difference formula can be used to simplify the square root calculation.
This is also the most basic and common problem in our quadratic root reduction calculation.
Variant problem 1: this is a classic problem of simplifying quadratic roots by multiplication formula, and it is also a common method of simplifying quadratic roots.
If the root sign happens to be a completely flat path, then it should be turned into a completely flat path first, and then the square of the quadratic root can be directly expressed in the form of absolute value.
According to the meaning of the question, judge whether the algebraic expression in the absolute value is positive or negative. If it is an integer, it is equal to itself. If it is negative, it is equal to its reciprocal.
Tip 2: Simplify triangles by using trilateral relations. Using the double non-negative property of quadratic root, the square root of the root is equal to the absolute value after its square.
Using the trilateral relationship of a triangle, its positive and negative can be determined. If it is a positive number, it is equal to itself. If it is negative, it is equal to its reciprocal.
Tip 3: Simplify with denominator, which is also one of the commonly used methods.
The denominator is physical and chemical, that is, the square root of denominator, numerator and denominator can be determined by applying the square difference formula.
There are many such questions and many variant questions. Students should think more and summarize more when they do their own problems. Start with simple basic questions, gradually increase the difficulty, and slowly do some expansion and training questions. By analogy, practice makes perfect, and test scores will naturally improve.
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