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

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

Exercise Evaluate √ 169. 13

Exercise Evaluate – √ 81. – 9

Exercise Evaluate √ – 121. no real solution

√ x = 5 x2 = 25

√ x2 = ± x “plus or minus”

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

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

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

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

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

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

Example Solve x2 = 25. x = ± 5

Example Solve x2 = 0.25. x = ± 0.5

Example Solve y2 + 100 = 149. y = ± 7

Example Solve 4y2 = 144. y = ± 6

Example Solve 3x2 + 15 = 9. no real solution

Example Solve 2x2 + 4 = 36. x = ± 4

Example Solve (2x)2 + 4 = 20. x = ± 2

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

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

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

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