1. Section 8.5 and 8.6 Multiplying and Dividing Radicals/Solving Radical Equations

2. Multiplying Radicals Multiplying radicals utilizes the previously- discussed concepts: The distributive property The FOIL method Simplifying radicals Combining like radical terms

3. The Rules

4. Be Careful!!! Do not confuse the rules for multiplication with the rules for addition.

5. Examples

6. Dividing Radicals Dividing radicals is actually not division. Rationalizing the denominator is the process of removing radicals from the denominator. There are two cases for rationalizing the denominator.

7. Case 1: One term in the denominator Multiply numerator and denominator by the term in the denominator.

8. Case 2: Two terms in the denominator Multiply numerator and denominator by the conjugate of the denominator.

9. Solving Radical Equations 1.Isolate the radical expression, if possible. 2.Raise each side of the equation to a power equal to the index. 3.Solve the resulting equation: a. If linear, isolate the variable b. If quadratic, solve by factoring 4. If you have more than one solution, sometimes one of them won’t work. You might want to check them.

10. Examples

11. More Examples