Topic VIII: Radical Functions and Equations 8.1 Solving Radical Equations

Solve. Solution: It is important to note that even though the algebraic work may be done perfectly, the answer produced may not make the original equation true. Slide EXAMPLE 1 Using the Squaring Property of Equality

Solve. Solution: Slide EXAMPLE 2 Using the Squaring Property with a Radical on Each Side

Solution: Solve. False Because we get a false statement when we checked x = 16, this is called an extraneous solution. Therefore there is no solution. Check: Slide EXAMPLE 3 Using the Squaring Property When One Side Is Negative

Solving a Radical Equation Step 1Isolate a radical. Arrange the terms so that a radical is isolated on one side of the equation. Solving a Radical Equation. Step 6Check all proposed solutions in the original equation. Step 5Solve the equation. Find all proposed solutions. Step 4Repeat Steps 1-3 if there is still a term with a radical. Step 3Combine like terms. Step 2Raise both sides to the power of the index. Slide

Solution: Solve When we substitute x into the original equation we get another extraneous solution, the solution set is Slide EXAMPLE 4 Using the Squaring Property with a Quadratic Expression

Solve Solution: or Slide EXAMPLE 5 Using the Squaring Property when One Side Has Two Terms

Solve. Solution: The solution set is {4,9}. or Slide EXAMPLE 6 Rewriting an Equation before Using the Squaring Property

Solve. Solution: The solution set is {8}. Slide EXAMPLE 7 Using the Squaring Property Twice

Solve each equation. Solution: or Slide EXAMPLE 8 Solving Equations with Cube Root Radicals

Just Keep Practicing !!!