Algebra 1 Common Core Student Edition, Grade 8-9

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9. A radical expression is in simplified form if the radicand
   has no perfect-square factors other than 1 , the radicand
   contains no fractions, and no radicals appear in the
   denominator of a fraction.
   Ex e r c i se s 11. 3VTT 13. -2VT5 15. 50 V7


10. 5f2 V2f 19. -63x4V3x 21. -18y V3y 23. 4


11. 30 27. 42n2 29. 16y3 31. -126aVa 33. 24c7


12. w V26 37. 39. 41. 2Za 43. V p


13. 2VTT 47. 4 49. 2 V 6 in. 51. not simplest form;
    radical in the denominator of a fraction 53. Simplest
    form; radicand has no perfect-square factors other than 1.
    55a. fV3f b.iC.^f d.^ 57a. VW VO =
    V180 = V36 • VS = 6 VS b. Answers may vary.
    Sample: 4 and 45 59. 2 VTI 61. 63. Vy
    y


14. 4V5 67. ab2cVabc 69. ^ 71. 1 ± Vs


15. Answers may vary. Sample: 12, 27, 48 7 5. 10b 2
    77a. 5 ( ^ ) ft, 3.99 ft b. 4 ( ^ j , 3.19 in.
    c. ( ^ P 7) m, 1.78 m

Lesson 10-3 pp. 626-631

Go t It? 1a. - V 2 b. 7 V 5 2a. 8 V 7 b. 8V2

c. No; if they are unlike and have no common factors

other than 1 , even if they can be simplified, they still will

not be like. 3a. 2 V 3 + 5 V 2 b. 15 - 4VTT

c. - 6 V 2 - 6 4. ~ 3VTo + 3V5 5 _ ( 6 V ^ _ 6) j n^ Qr

about 7.4 in.

Lesso n Ch eck 1. 5V3 2. V 6 3. V2T-2V7

4. 41 - 12V5 5. 3 V 5 - VTO 6. 2 V 7 - 4
   7a. VT3 + 2 b. V6-V3 c. V5 + VTO
   8. V3 • V3 # 9; 2Y ^ T = y ^ r 1
   Ex e r c i se s 9. 7 V 5 1 1. 8 V 3 1 3. 0 1 5. - 7 V 5
   17. 9VT0 19. 19V5 21.2V3 + 3V2 23.3V7-21


5. 5V33- 15V22 27. -6 29.

31

3V7 + 3V3

4

23 V 5 - 23

33. -2 V 5 - 5 35.
    ft, or about 14.2 ft 39.

62 - 20 V 6

7 V T3 - 7 V 5

41. V7] -0.4 43. 9 + 6 V 2 + 4 V 5 + 3 VTO;
    35.9 45. No; yes; you can simplify VT2 to 2 V 3 and
    then combine the like radicals. 47. 5VlO


42. 22V 3-6 51. 13 + V65 + VT30 + 5V2

-1.3

53. -24


54. 4V3 + 4V2 + 3V6-

b. x 2 Vx 61.iV 5-

h 6 57. sV 3 59a. X2
63a. 3V2 b. 2V7
c. V2{p + q) 65. H 67. The graph of the function
y = |x| is V-shaped with the vertex at the origin. The
domain is all real numbers and the range is {y |y > 0 },

0

Po w erAlg eb ra.com

because no matter w hat value of x you input, the output

will always be nonnegative. 68. 6\/3 69. 15V6

70.^ 71. 15 72. 816 73. 211 74. 527 75. 33

76. -1 77. -4, 3 78. -5, 3 79. -3, | 80. -2, \ 81. -7
    Lesson 10-4 pp. 633-638
    Go t It? 1 .9 2. 0.825 ft 3. 7 4. —2 5a. no solution
    b. The principal root of a number is never negative.
    Lesso n Ch eck 1 .12 2. 3 3. 1 4. no solution 5. C


77. If x 2 = y 2, then x = y; no, if x = - 1 and y = 1, then
    x 2 = y 2, but x + y.
    Ex e r c i se s 7. 4 9. 3 6 1 1. 8 1 3. 1 6 1 5. - 2 17. about
    5.2 ft 19. 4.5 21. 7 23. 4 25. 2 27. none 29. -7


78. 3 33. no solution 35. no solution 37. The student
    did not check the solutions in the original equations. Both
    of those solutions are extraneous, so the equation has no
    solution. 39a. 25 b. 11.25 41. Add Vy + 2 to each side
    of the equation. Square each side of the equation. Solve
    fory. Check each apparent solution in the original
    equation. 43.3 45. no solution 47. 1.5 49. 1600 ft


79. The square of V x - 1 will have only two terms, while
    the square of V x - 1 will have three terms.


80. 5 V 2 58. -2 4 59. -? V3 4 V?
    3


81. D 55.


82. no solution 61. - 2 , 2 62. - |


83. V

\VV

-2^3

64.

V

65. y

\

\

3

Lesson 10-5 pp. 639-644

Go t It? 1 , x < 2.5 2a. when the power is more than

56.25 watts b. 4

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