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# 9.1E: Exercises

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### Practice Makes Perfect

In the following exercises, solve each equation.

1. $$a^{2}=49$$

2. $$b^{2}=144$$

3. $$r^{2}-24=0$$

4. $$t^{2}-75=0$$

5. $$u^{2}-300=0$$

6. $$v^{2}-80=0$$

7. $$4 m^{2}=36$$

8. $$3 n^{2}=48$$

9. $$\frac{4}{3} x^{2}=48$$

10. $$\frac{5}{3} y^{2}=60$$

11. $$x^{2}+25=0$$

12. $$y^{2}+64=0$$

13. $$x^{2}+63=0$$

14. $$y^{2}+45=0$$

15. $$\frac{4}{3} x^{2}+2=110$$

16. $$\frac{2}{3} y^{2}-8=-2$$

17. $$\frac{2}{5} a^{2}+3=11$$

18. $$\frac{3}{2} b^{2}-7=41$$

19. $$7 p^{2}+10=26$$

20. $$2 q^{2}+5=30$$

21. $$5 y^{2}-7=25$$

22. $$3 x^{2}-8=46$$

1. $$a=\pm 7$$

3. $$r=\pm 2 \sqrt{6}$$

5. $$u=\pm 10 \sqrt{3}$$

7. $$m=\pm 3$$

9. $$x=\pm 6$$

11. $$x=\pm 5 i$$

13. $$x=\pm 3 \sqrt{7} i$$

15. $$x=\pm 9$$

17. $$a=\pm 2 \sqrt{5}$$

19. $$p=\pm \frac{4 \sqrt{7}}{7}$$

21. $$y=\pm \frac{4 \sqrt{10}}{5}$$

In the following exercises, solve each equation.

23. $$(u-6)^{2}=64$$

24. $$(v+10)^{2}=121$$

25. $$(m-6)^{2}=20$$

26. $$(n+5)^{2}=32$$

27. $$\left(r-\frac{1}{2}\right)^{2}=\frac{3}{4}$$

28. $$\left(x+\frac{1}{5}\right)^{2}=\frac{7}{25}$$

29. $$\left(y+\frac{2}{3}\right)^{2}=\frac{8}{81}$$

30. $$\left(t-\frac{5}{6}\right)^{2}=\frac{11}{25}$$

31. $$(a-7)^{2}+5=55$$

32. $$(b-1)^{2}-9=39$$

33. $$4(x+3)^{2}-5=27$$

34. $$5(x+3)^{2}-7=68$$

35. $$(5 c+1)^{2}=-27$$

36. $$(8 d-6)^{2}=-24$$

37. $$(4 x-3)^{2}+11=-17$$

38. $$(2 y+1)^{2}-5=-23$$

39. $$m^{2}-4 m+4=8$$

40. $$n^{2}+8 n+16=27$$

41. $$x^{2}-6 x+9=12$$

42. $$y^{2}+12 y+36=32$$

43. $$25 x^{2}-30 x+9=36$$

44. $$9 y^{2}+12 y+4=9$$

45. $$36 x^{2}-24 x+4=81$$

46. $$64 x^{2}+144 x+81=25$$

23. $$u=14, u=-2$$

25. $$m=6 \pm 2 \sqrt{5}$$

27. $$r=\frac{1}{2} \pm \frac{\sqrt{3}}{2}$$

29. $$y=-\frac{2}{3} \pm \frac{2 \sqrt{2}}{9}$$

31. $$a=7 \pm 5 \sqrt{2}$$

33. $$x=-3 \pm 2 \sqrt{2}$$

35. $$c=-\frac{1}{5} \pm \frac{3 \sqrt{3}}{5} i$$

37. $$x=\frac{3}{4} \pm \frac{\sqrt{7}}{2} i$$

39. $$m=2 \pm 2 \sqrt{2}$$

41. $$x=3+2 \sqrt{3}, x=3-2 \sqrt{3}$$

43. $$x=-\frac{3}{5}, x=\frac{9}{5}$$

45. $$x=-\frac{7}{6}, x=\frac{11}{6}$$

In the following exercises, solve using the Square Root Property.

47. $$2 r^{2}=32$$

48. $$4 t^{2}=16$$

49. $$(a-4)^{2}=28$$

50. $$(b+7)^{2}=8$$

51. $$9 w^{2}-24 w+16=1$$

52. $$4 z^{2}+4 z+1=49$$

53. $$a^{2}-18=0$$

54. $$b^{2}-108=0$$

55. $$\left(p-\frac{1}{3}\right)^{2}=\frac{7}{9}$$

56. $$\left(q-\frac{3}{5}\right)^{2}=\frac{3}{4}$$

57. $$m^{2}+12=0$$

58. $$n^{2}+48=0$$

59. $$u^{2}-14 u+49=72$$

60. $$v^{2}+18 v+81=50$$

61. $$(m-4)^{2}+3=15$$

62. $$(n-7)^{2}-8=64$$

63. $$(x+5)^{2}=4$$

64. $$(y-4)^{2}=64$$

65. $$6 c^{2}+4=29$$

66. $$2 d^{2}-4=77$$

67. $$(x-6)^{2}+7=3$$

68. $$(y-4)^{2}+10=9$$

47. $$r=\pm 4$$

49. $$a=4 \pm 2 \sqrt{7}$$

51. $$w=1, w=\frac{5}{3}$$

53. $$a=\pm 3 \sqrt{2}$$

55. $$p=\frac{1}{3} \pm \frac{\sqrt{7}}{3}$$

57. $$m=\pm 2 \sqrt{2 i}$$

59. $$u=7 \pm 6 \sqrt{2}$$

61. $$m=4 \pm 2 \sqrt{3}$$

63. $$x=-3, x=-7$$

65. $$c=\pm \frac{5 \sqrt{6}}{6}$$

67. $$x=6 \pm 2 i$$

69. In your own words, explain the Square Root Property.

70. In your own words, explain how to use the Square Root Property to solve the quadratic equation $$(x+2)^{2}=16$$.

## Self Check

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

Choose how would you respond to the statement “I can solve quadratic equations of the form a times the square of $$x$$ minus $$h$$ equals $$k$$ using the Square Root Property.” “Confidently,” “with some help,” or “No, I don’t get it.”