8.7E: Exercises
 Page ID
 30331
Practice Makes Perfect
In the following exercises, solve.
1. \(\sqrt{5 x6}=8\)
2. \(\sqrt{4 x3}=7\)
3. \(\sqrt{5 x+1}=3\)
4. \(\sqrt{3 y4}=2\)
5. \(\sqrt[3]{2 x}=2\)
6. \(\sqrt[3]{4 x1}=3\)
7. \(\sqrt{2 m3}5=0\)
8. \(\sqrt{2 n1}3=0\)
9. \(\sqrt{6 v2}10=0\)
10. \(\sqrt{12 u+1}11=0\)
11. \(\sqrt{4 m+2}+2=6\)
12. \(\sqrt{6 n+1}+4=8\)
13. \(\sqrt{2 u3}+2=0\)
14. \(\sqrt{5 v2}+5=0\)
15. \(\sqrt{u3}+3=u\)
16. \(\sqrt{v10}+10=v\)
17. \(\sqrt{r1}=r1\)
18. \(\sqrt{s8}=s8\)
19. \(\sqrt[3]{6 x+4}=4\)
20. \(\sqrt[3]{11 x+4}=5\)
21. \(\sqrt[3]{4 x+5}2=5\)
22. \(\sqrt[3]{9 x1}1=5\)
23. \((6 x+1)^{\frac{1}{2}}3=4\)
24. \((3 x2)^{\frac{1}{2}}+1=6\)
25. \((8 x+5)^{\frac{1}{3}}+2=1\)
26. \((12 x5)^{\frac{1}{3}}+8=3\)
27. \((12 x3)^{\frac{1}{4}}5=2\)
28. \((5 x4)^{\frac{1}{4}}+7=9\)
29. \(\sqrt{x+1}x+1=0\)
30. \(\sqrt{y+4}y+2=0\)
31. \(\sqrt{z+100}z=10\)
32. \(\sqrt{w+25}w=5\)
33. \(3 \sqrt{2 x3}20=7\)
34. \(2 \sqrt{5 x+1}8=0\)
35. \(2 \sqrt{8 r+1}8=2\)
36. \(3 \sqrt{7 y+1}10=8\)
 Answer

1. \(m=14\)
3. no solution
5. \(x=4\)
7. \(m=14\)
9. \(v=17\)
11. \(m=\frac{7}{2}\)
13. no solution
15. \(u=3, u=4\)
17. \(r=1, r=2\)
19. \(x=10\)
21. \(x=8\)
23. \(x=8\)
25. \(x=4\)
27. \(x=7\)
29. \(x=3\)
31. \(z=21\)
33. \(x=42\)
35. \(r=3\)
In the following exercises, solve.
37. \(\sqrt{3 u+7}=\sqrt{5 u+1}\)
38. \(\sqrt{4 v+1}=\sqrt{3 v+3}\)
39. \(\sqrt{8+2 r}=\sqrt{3 r+10}\)
40. \(\sqrt{10+2 c}=\sqrt{4 c+16}\)
41. \(\sqrt[3]{5 x1}=\sqrt[3]{x+3}\)
42. \(\sqrt[3]{8 x5}=\sqrt[3]{3 x+5}\)
43. \(\sqrt[3]{2 x^{2}+9 x18}=\sqrt[3]{x^{2}+3 x2}\)
44. \(\sqrt[3]{x^{2}x+18}=\sqrt[3]{2 x^{2}3 x6}\)
45. \(\sqrt{a}+2=\sqrt{a+4}\)
46. \(\sqrt{r}+6=\sqrt{r+8}\)
47. \(\sqrt{u}+1=\sqrt{u+4}\)
48. \(\sqrt{x}+1=\sqrt{x+2}\)
49. \(\sqrt{a+5}\sqrt{a}=1\)
50. \(2=\sqrt{d20}\sqrt{d}\)
51. \(\sqrt{2 x+1}=1+\sqrt{x}\)
52. \(\sqrt{3 x+1}=1+\sqrt{2 x1}\)
53. \(\sqrt{2 x1}\sqrt{x1}=1\)
54. \(\sqrt{x+1}\sqrt{x2}=1\)
55. \(\sqrt{x+7}\sqrt{x5}=2\)
56. \(\sqrt{x+5}\sqrt{x3}=2\)
 Answer

37. \(u=3\)
39. \(r=2\)
41. \(x=1\)
43. \(x=8, x=2\)
45. \(a=0\)
47. \(u=\frac{9}{4}\)
49. \(a=4\)
51. \(x=0\: x=4\)
53. \(x=1\: x=5\)
55. \(x=9\)
In the following exercises, solve. Round approximations to one decimal place.
 Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of \(75\) square feet. Use the formula \(s=\sqrt{A}\) to find the length of each side of his garden. Round your answer to the nearest tenth of a foot.
 Landscaping Vince wants to make a square patio in his yard. He has enough concrete to pave an area of \(130\) square feet. Use the formula \(s=\sqrt{A}\) to find the length of each side of his patio. Round your answer to the nearest tenth of a foot.
 Gravity A hang glider dropped his cell phone from a height of \(350\) feet. Use the formula \(t=\frac{\sqrt{h}}{4}\) to find how many seconds it took for the cell phone to reach the ground.
 Gravity A construction worker dropped a hammer while building the Grand Canyon skywalk, \(4000\) feet above the Colorado River. Use the formula \(t=\frac{\sqrt{h}}{4}\) to find how many seconds it took for the hammer to reach the river.
 Accident investigation The skid marks for a car involved in an accident measured \(216\) feet. Use the formula \(s=\sqrt{24d}\) to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.
 Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was \(175\) feet. Use the formula \(s=\sqrt{24d}\) to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.
 Answer

57. \(8.7\) feet
59. \(4.7\) seconds
61. \(72\) feet
 Explain why an equation of the form \(\sqrt{x}+1=0\) has no solution.

 Solve the equations \(\sqrt{r+4}r+2=0\).
 Explain why one of the "solutions" that was found was not actually a solution to the equation.
 Answer

63. Answers will vary.
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. After reviewing this checklist, what will you do to become confident for all objectives?