1. Exercise
Every positive number has how many real square roots? 2

2. Exercise
Every negative number has how many real square roots?
none

3. Exercise
Evaluate √ 169. 13

4. Exercise
Evaluate – √ 81.
– 9

5. Exercise
Evaluate √ – 121.
no real solution

6. √ x = 5
x2 = 25

7. √ x2 = ± x
“plus or minus”

8. Example 1
Solve x2 = 16.
x2 = 16
√ x2 = ± √ 16
x = ± 4

9. Solving Equations of the Form x2 = a
If x2 = a and a > 0, then x = ± √ a.

10. Example 2
Solve x2 = 49.
x2 = 49
√ x2 = ± √ 49
x = ± 7

11. Example 3 Solve x2 – 4 = – 3. x2 – 4 = – 3 x2 – 4 + 4 = – 3 + 4 x2 = 1

12. Example 4 Solve 3x2 – 12 = 18. 3x2 – 12 = 18 3x2 – 12 + 12 = 18 + 12

13. Example 5 Solve x2 + 21 = 12. x2 + 21 = 12 x2 + 21 – 21 = 12 – 21
no real solution

14. Example
Solve x2 = 25.
x = ± 5

15. Example
Solve x2 = 0.25.
x = ± 0.5

16. Example
Solve y = 149.
y = ± 7

17. Example
Solve 4y2 = 144.
y = ± 6

18. Example
Solve 3x = 9.
no real solution

19. Example
Solve 2x2 + 4 = 36.
x = ± 4

20. Example
Solve (2x)2 + 4 = 20.
x = ± 2

21. Example
Solve 2(x2 + 4) = 36.
x = ± √ 14

22. Exercise
Solve (x + 4)2 = 16.
x = – 8, 0

23. Exercise
Solve (2x – 5)2 = 49.
x = – 1, 6

24. Exercise
Solve (6x – 7)2 = 4.
x = ,
3 2
5 6