Objective: Solve radical equations by performing the principal of squaring and checking the solutions.
Solving radical equations requires us to understand a new algebraic principal, the principal of squaring. The principal of squaring states that you can square both sides of an equation when solving an equation. When put into a step-by-step approach, you can solve radical equations by:
1) Isolating the radical term
2) Performing the principal of squaring
3) Solving the resulting equations
4) Checking the possible solutions with the original equation.
Step 4, checking the possible solutions with the original equation is an important and necessary step when using the principal of squaring, because it is possible to get possible solutions that are not actual solutions when checked. What the video below to see these four steps in action and also see why checking the possible solutions is a necessary step when solving radical equations.
Only proceed to this second part of solving radical equations if you have already learned how to solve quadratic equations (see Unit 8).
Sometimes after performing the principal of squaring on a radical equation, you will end up with a quadratic equation that must be solved. The same four steps apply when solving the radical equation, but you must now solve the resulting quadratic equation and then check all the possible solutions (since there may be more than one). Watch the video below to see examples of this slight variation.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.