1. Topic VIII: Radical Functions and Equations 8.1 Solving Radical Equations

4. 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 8.6-6 EXAMPLE 1 Using the Squaring Property of Equality

5. Solve. Solution: Slide 8.6-7 EXAMPLE 2 Using the Squaring Property with a Radical on Each Side

6. 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 8.6-9 EXAMPLE 3 Using the Squaring Property When One Side Is Negative

7. 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 8.6-10

8. Solution: Solve When we substitute x into the original equation we get another extraneous solution, the solution set is Slide 8.6-11 EXAMPLE 4 Using the Squaring Property with a Quadratic Expression

9. Solve Solution: or Slide 8.6-13 EXAMPLE 5 Using the Squaring Property when One Side Has Two Terms

10. Solve. Solution: The solution set is {4,9}. or Slide 8.6-14 EXAMPLE 6 Rewriting an Equation before Using the Squaring Property

11. Solve. Solution: The solution set is {8}. Slide 8.6-16 EXAMPLE 7 Using the Squaring Property Twice

12. Solve each equation. Solution: or Slide 8.6-19 EXAMPLE 8 Solving Equations with Cube Root Radicals

15. Just Keep Practicing !!!