1/6 number-shape combination method.
Combine coordinate axes with mathematical expressions to achieve the purpose of rapid simplification.
2/6 formula method.
According to the known conditions of the topic, through the methods of deformation and integration, an available formula is compiled and solved quickly.
3/6 replacement method.
According to the known conditions, we use unknown variables instead of regular expressions to find rules and solve them quickly.
4/6 total replacement method.
Based on the known conditions, the expression values related to solving the expression are obtained by addition, subtraction, multiplication and division, and are substituted as a whole.
5/6 matching method.
Through a series of deformation, simplification and integration, the solution is made into a formula and solved by the formula.
6/6 auxiliary element method.
According to the known conditions, take a numerical value greater than 0 instead of the known variable, and convert it into this numerical relationship through correlation to solve it quickly.
There are two ways to simplify a quadratic root into the simplest quadratic root: if the root number is algebraic or integer, first decompose it into factors or factorization factors, and then expel the root number from the completely flat path or square number to simplify the root. If the root sign is a fraction or decimal (including decimal), the denominator should be rationalized first, and then simplified according to the situation that the root sign is an algebraic expression or an integer.
Skills of simplifying quadratic roots
The steps of simplifying quadratic roots can be simply summarized as "opening" and "filling".
The first step is "open", that is, in each factor of the open mode, it can be replaced by their arithmetic square roots, and everything that can be moved outside the root number can be moved outside the root number, so that the index of each factor of the newly opened mode is less than the root index 2;
The second step is "complement", that is, the denominator and numerator of the newly opened mode are multiplied by the denominator itself at the same time, so that after the denominator is multiplied by itself, the new denominator can all leave the root sign outside, thus achieving the purpose of opening the mode without the denominator.