Web page link
Quadratic radical:
Generally speaking, algebraic expressions with the shape √a are called quadratic radicals, where a? This is called the root sign. When a≥0, √a represents the arithmetic square root of a; When a is less than 0, the value of √a is purely imaginary (in the root formula of a quadratic equation with one variable, if it is negative under the root sign, the equation has two conjugate imaginary roots).
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.
The simplest quadratic root condition: the factor of root sign is integer or letter, and the factor is algebraic expression; The root sign does not contain a factor or a factor that can be converted into a square number or a flat way.
The general steps of quadratic radical simplification are: turning a fraction or decimal into a false fraction; Decompose the root sign into prime factor or factorization factor; Move the factors or factors that can be fully opened in the root number to the outside of the root number; Remove the denominator in the root sign, or remove the root sign in the denominator; About integrals.
The application of quadratic roots is mainly reflected in two aspects: using the important thinking method from special to general and then from general to special to solve some regular exploratory problems; The quadratic root formula is used to solve the calculation problem of length and height. According to the known quantity, some lengths or heights can be obtained, or a material-saving scheme can be designed, and graphics can be spliced and divided. This process needs to calculate the quadratic root, which is actually a simplified evaluation.