Solving Radical Equations
Rule 1: To solve an equation with radicals:
Step 1: Determine the condition
Step 2: Isolate the radical
Step 3: Apply the power rule (raise both sides of the equation to the same power)
Step 4: Solve the resulting equation
Step 5: Check all solutions in the original equation
Definition 1: By raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. These solutions are called extraneous solutions.
Check your results for an extraneous solution - remembering that:
- a) an even index represents a positive root
- b) a negative radicand with an even index yields “NO REAL SOLUTION”
Find out more about solving radical equations below.
Practice: Answer the exercises below by solving simple radical equations in which only one radical contains a variable.