1. S OLVING R ADICAL E QUATIONS Objective: solve simple radical equations and check for extraneous solutions How do you undo a square root or a cube root?

2. V OCABULARY Radical Symbol

3. Square Root Ex. 9 = 3 ∙ 3 Cube Root Ex. 8 = 2 ∙ 2 ∙ 2 Fourth Root etc.

4. R ATIONAL (F RACTION ) E XPONENTS

5. R E - WRITE EACH IN RADICAL FORM :

6. R EMEMBER … A square root “undoes” a square A cube root “undoes” a cube

7. T HEREFORE … A square “undoes” a square root A cube “undoes” a cube root

8. H OW TO SOLVE A RADICAL EQUATION Step 1: Step 1: Put in radical form if necessary Step 2: Step 2: Get radical symbol alone Step 3: Step 3: Square or cube both sides Step 4: Step 4: Drop the radical symbol Step 5: Step 5: Solve Step 6: Step 6: Check your answers!! *Might be extraneous

9. E X 1) S OLVE FOR X

10. E X 2) S OLVE FOR X

11. E X 3) S OLVE FOR X

12. E X 4) S OLVE FOR X

13. S OLVE & C HECK S OLUTIONS x = 17

14. S OLVE & C HECK S OLUTIONS x = 6

15. S OLVE & C HECK S OLUTIONS x = 64

16. S OLVE & C HECK S OLUTIONS x = -1

17. S OLVE & C HECK S OLUTIONS x = 59

18. S OLVE & C HECK S OLUTIONS x = 727

19. S OLVE & C HECK S OLUTIONS x = 1 x = 4

20. S OLVE & C HECK S OLUTIONS x = -2 extraneous x = 1

21. S OLVE & C HECK S OLUTIONS No Solution