1. Transform equation: move the expression in the root sign to one side of the equation, so that there is only one root sign term in the equation. For example, if there are multiple radical terms in the equation, we can consider moving terms and merging similar terms to simplify them into one radical term.
2. Eliminate the root sign: square or power the two sides of the equation and eliminate the square of the root sign. However, it should be noted that the power operation on both sides of the equation will introduce new possible solutions, so it is necessary to test the obtained equation to eliminate misunderstandings.
3. Solving the equation: further algebraic operation will be carried out on the equation after the root number item is processed, and the unknown quantity will be solved from the root number. The specific solution depends on the form of the equation, which may involve operations such as distribution law, merging similar terms, shifting terms and simplification. According to the concrete form of the equation, we can use quadratic equation, linear equation and quadratic equation to solve it.
4. Test the feasibility of the solution: substitute the obtained solution into the original equation to verify whether it conforms to the original equation. Sometimes the solution of radical equation may introduce unreal solution or be limited to a certain range, so it is necessary to check the range and feasibility.
It should be noted that complex solutions may be involved in solving equations with root signs. In the case of true solution, the results can be filtered by appropriate conditions. In the case of complex solutions, complex forms of solutions can be preserved.
In a word, solving the equation with root sign needs to deform and simplify the equation, and then carry out further algebraic operation according to the concrete form and solution method of the equation. For more complex equations, you may need to use more advanced mathematical skills to solve them.
To sum up, the steps to solve the equation with root sign are as follows:
Eliminate the root sign and square both sides of the equation.
Move items: move items with variables to one side of the equation and other items to the other side of the equation.
Solve the variable, divide both sides of the equation by the coefficient of the variable, and get the final solution.
Of course, this is just one of the common solutions to the radical equation. For more complex radical equations, different methods may be needed, such as flat method and method of substitution method. However, through this basic solution, you have mastered the key skills to understand most radical equations.