If a quadratic radical satisfies the following two conditions: 1, the number of roots does not contain factors or can be opened to the largest factor; 2. The factor of the root sign is an integer and the factor is an algebraic expression. Then, this radical is called the simplest quadratic radical. ?
The main method to judge whether a quadratic root is the simplest quadratic root is according to the definition of the simplest quadratic root, or intuitively observing that the index of each factor (or factor) of the root number is less than the root index 2, and the root number does not contain the denominator. When the root number is polynomial, factorization should be carried out first, and then observation should be carried out.
Quadratic radical is the basis of learning quadratic equation and quadratic function, which is closely related to Pythagorean theorem, algebraic expression and other knowledge. According to the latest textbooks published by People's Education Publishing House and Zhejiang Education Publishing House, students in Grade Two will learn the second radical next semester.
Therefore, junior high school mathematics teaching requires students to master the simplification of quadratic roots, which is a must for graduation and senior high school entrance examination. Main problem-solving skills: proper use of the properties of quadratic roots, substitution, decomposition and elimination, factorization and overall substitution.
Simplify the process
1. If the root number is an algebraic expression or integer, first decompose it into factors or factorization factors, and then expel completely flat or square numbers from the root number to simplify the root number.
2. If the root sign is a fraction or decimal (including decimal), the denominator should be rationalized first, and then simplified according to the fact that the root sign is an algebraic expression or an integer.
It can be seen that there are two main points in simplifying the quadratic root: first, the denominator is reasonable; The second is the factorization factor, which gives a root sign to a completely flat road (number).