1. Simplifying Radical Expressions Simplifying Radicals Radicals with variables

2. Definition of Square Root: For any real numbers a and b, if a 2 = b, then a is a square root of b. Index number Radical sign radicand Radical Expression

3. Let’s review. Simplify each expression. Assume all values of the variable are positive. Examples:

5. Try these with your partner:

7. Adding and Subtracting Radical Expressions

8. Radical expressions can be combined (added or subtracted) if they are like radicals – that is, they have the same root ________ and the same ________. Example 5: and are alike. The root index is _____ for both expressions and the radicand is _____ for both expressions. index radicand 2 6

9. Example 6: and are not alike. They both have the same __________ but the root _______ are not the same. To determine whether two radicals are like radicals, you must first __________ each radicand. indices radicand simplify

10. Simplify each expression: (7). (8). (9). (10).

11. Try these with your partner: (11). (12). (13). (14).

12. Add or subtract as indicated. Simplify first! (15).

13. (16).

14. Try these with your partner: (17).

15. (18).

16. (19).

17. (20).