See Problems 4 and 5.

Tell which solutions, if any, are extraneous for each equation.

25. − z = − z + 6 ; z = − 3 , z = 2 negative z equals . square root of negative z plus 6 end root . semicolon z equals negative 3 comma z equals 2
26. 12 − n = n ; n = − 4 , n = 3 square root of 12 minus n end root , equals n semicolon n equals negative 4 comma n equals 3
27. y = 2 y ; y = 0 , y = 2 y equals , square root of 2 y end root , semicolon y equals 0 comma y equals 2
28. 2 a = 4 a + 3 ; a = 3 2 , a = − 1 2 2 eh equals . square root of 4 eh plus 3 end root . semicolon eh equals , 3 halves , comma eh equals negative , 1 half
29. x = 28 − 3 x ; x = 4 , x = − 7 x equals . square root of 28 minus 3 x end root . semicolon x equals 4 comma x equals negative 7
30. − t = − 6 t − 5 ; t = − 5 , t = − 1 negative t equals . square root of negative 6 t minus 5 end root . semicolon t equals negative 5 comma t equals negative 1

Solve each radical equation. Check your solution. If there is no solution, write no solution.

31. x = 2 x + 3 x equals . square root of 2 x plus 3 end root
32. n = 4 n + 5 n equals . square root of 4 n plus 5 end root
33. 3 b = − 3 square root of 3 b end root , equals negative 3
34. 2 y = 5 y + 6 2 y equals . square root of 5 y plus 6 end root
35. − 2 2 r + 5 = 6 negative 2 . square root of 2 r plus 5 end root . equals 6
36. d + 12 = d square root of d plus 12 end root , equals d

B Apply

37. Error Analysis A student solved the equation r = − 6 r − 5 r equals . square root of negative 6 r minus 5 end root  and found the solutions − 1 negative 1  and − 5 . negative 5 .  Describe and correct the student's error.
38. Think About a Plan The total surface area A of Earth, in square kilometers, is related to Earth's radius r, in kilometers, by r = A 4 π . r equals , square root of fraction eh , over 4 pi end fraction end root , .  Earth's radius is about 6378 km. What is its surface area? Round to the nearest square kilometer.
    • What equation in one variable can you solve to find Earth's surface area?
    • How can you check the reasonableness of your solution?

39. Geometry In the right triangle Δ A B C , cap delta eh b c comma  the altitude C D ¯ c d bar  is at a right angle to the hypotenuse. You can use C D = ( A D ) ( D B ) c d equals . square root of open , eh d , close . open , d b , close end root  to find missing lengths.

    

    1. Find AD if CD = 10 and DB = 4.
    2. Find DB if AD = 20 and CD = 15.
40. Packaging The radius r of a cylindrical can with volume V and height h is given by r = V π h . r equals , square root of fraction v , over pi h end fraction end root , .  What is the height of a can with a radius of 2 in. and a volume of 75  in . 3 ? 75 , in , . cubed , question mark
41. Writing Explain how you would solve the equation 2 y − y + 2 = 0. square root of 2 y end root , minus , square root of y plus 2 end root , equals 0.
42. Open-Ended Write two radical equations that have 3 for a solution.

Solve each radical equation. Check your solution. If there is no solution, write no solution.

43. 5 x + 10 = 5 square root of 5 x plus 10 end root . equals 5
44. − 6 − 3 y = − 3 negative 6 minus , square root of 3 y end root , equals negative 3
45. 7 p + 5 = p − 3 square root of 7 p plus 5 end root . equals , square root of p minus 3 end root
46. a = 7 a − 6 eh equals . square root of 7 eh minus 6 end root
47. y + 12 = 3 y square root of y plus 12 end root , equals 3 square root of y
48. 3 − 4 a + 1 = 12 3 minus . square root of 4 eh plus 1 end root . equals 12
49. Physics The formula t = n 16 t equals , square root of n over 16 end root  gives the time t in seconds for an object that is initially at rest to fall n feet. What is the distance an object falls in the first 10 s?

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