1. Principle of Square Roots

2. For any nonnegative real number k, if x 2 = k, then x = or x =. -

3. x x 2 = 9 3 = like x 2 – 9 = 0 (x + 3)(x – 3) = 0 {± 3 } x 2 = 9

4. x x 2 = 100 10 = like x 2 – 100 = 0 (x + 10)(x – 10) = 0 {± 10 } x 2 = 100

5. x x 2 = 14 14 = like x 2 – 14 = 0 (x + )(x – ) = 0 Can’t factor. Answers are not rational. x 2 = 14

6. x x 2 = 29 29 = x 2 = 29 like x 2 – 29 = 0 (x + )(x – ) = 0 Can’t factor. Answers are not rational.

7. x x 2 = -1 i = like x 2 + 1 = 0 (x )(x ) = 0 Can’t factor. Answers are not rational.

8. x x 2 = -16 4i4i =

9. x x 2 = = 9x 2 = 25 x = 25 9

10. x x 2 = = 16x 2 = 49 x = 49 16

11. x x 2 = = 9x 2 = 13 x =

12. x x 2 = = 16x 2 = 41 x =

13. x x 2 = = 3x 2 = 2 x =

14. x x 2 = = 5x 2 = 11 x =

15. x x 2 = 8 8 = x = 2·2·2 x =22

16. x x 2 = 12 12 = x 2 = 12 x = 2·2·3 x = 23

17. x x 2 = 32 32 = x 2 = 32 x = 2·2·2·2·2 x = 4 22·22 x =

18. x x 2 = -20 -20 = x 2 = -20 x = -2·2·5 x = 2i2i5

19. x x 2 = -24 -24 = x 2 = -24 x = -2·2·6 x= 2i2i6 -2·2·2·3

20. x x 2 = 0 0 = x = 0 dr

21. x x 2 = = 7x 2 = 32 x = x = x = Wow!

22. x x 2 = = 18x 2 = -1 x = x = x = Double wow!

23. That’s all!