1. Solving Radical Equations Chapter 7.6

2. What is a Radical Equation? A Radical Equation is an equation that has a variable in a radicand or has a variable expression with a rational exponent. yes no

3. Recall: Solving Quadratics How would you solve the following equation? Solve by taking the SQUARE ROOT of both sides. Why? Square roots and Squaring are inverse operations… they “undo” each other!

4. “Getting Rid” of the Radical Sign So… consider this: How could you solve for x now? Solve by doing the inverse operation: SQUARING!

5. Powers Property of Equality The key step in solving radical equations is raising both sides of the equation to the same power. If a = b, then a n = b n

6. Steps to Solving a Radical Equation 1.Isolate the Radical. 2.Raise both sides to the power equal to the index. 3.Solve for x. 4.Check your answer.

7. Example: Solving a Radical Equation + 4

8. Why Check My Answers? 2 () 2 NO SOLUTION Since 16 doesn’t plug in as a solution. Let’s Double Check that this works Note: You will get Extraneous Solutions from time to time – always do a quick check

9. Try One…