6-5 Operations with Radical Expressions. CCSS PRECISION Simplify. SOLUTION: SOLUTION: SOLUTION: esolutions Manual - Powered by Cognero Page 1

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2. CCSS PRECISION Simplify. 4. 6. esolutions Manual - Powered by Cognero Page 1

8. 10. 12. esolutions Manual - Powered by Cognero Page 2

14. 16. esolutions Manual - Powered by Cognero Page 3

Simplify. 18. 20. 22. esolutions Manual - Powered by Cognero Page 4

24. 26. 28. 30. esolutions Manual - Powered by Cognero Page 5

32. 34. GEOMETRY Find the perimeter of the rectangle. The perimeter of a rectangle of length l and width w is P = 2l + 2w. Therefore, the perimeter of the rectangle is ft. 36. GEOMETRY Find the exact surface area of a sphere with radius of inches. The surface area of a sphere of radius r is. The surface area of the sphere is square inches. esolutions Manual - Powered by Cognero Page 6

Simplify. 38. 40. 42. esolutions Manual - Powered by Cognero Page 7

44. 46. Simplify. 48. esolutions Manual - Powered by Cognero Page 8

50. 52. esolutions Manual - Powered by Cognero Page 9

54. APPLES The diameter of an apple is related to its weight and can be modeled by the formula, where d is the diameter in inches and w is the weight in ounces. Find the diameter of an apple that weighs 6.47 ounces. Substitute 6.47 for w and simplify. The diameter of the apple is about 2.69 inches. Simplify each expression if b is an even number. 56. 58. esolutions Manual - Powered by Cognero Page 10

60. ERROR ANALYSIS Twyla and Ben are simplifying. Is either of them correct? Explain your reasoning. Twyla is correct. Ben s mistakes were multiplying the 4 by 16 instead of 4 and multiplying the 6 by 9 instead of 3. 62. CCSS ARGUMENTS For what values of a is a real number? Explain. 0 is the only possible value for a since is defined for, and is defined for. 64. OPEN ENDED Find a number other than 1 that has a positive whole number for a square root, cube root, and fourth root. The LCM of 2, 3 and 4 is 12. Sample answer: 4096 esolutions Manual - Powered by Cognero Page 11

66. PROBABILITY A six-sided number cube has faces with the numbers 1 though 6 marked on it. What is the probability that a number less than 4 will occur on one toss of the number cube? A. B. C. D. There are 3 chances to get a number less than 4. The probability of getting a number less than 4 is. Option A is the correct answer. 68. SHORT RESPONSE Which property is illustrated by? Additive Identity Property Simplify. 70. esolutions Manual - Powered by Cognero Page 12

72. Solve each equation. 74. Let y = x 2. By the Zero Product Property: The solutions are 5, 3, 3 and 5. esolutions Manual - Powered by Cognero Page 13

76. Let y = x 2. By the Zero Product Property: The solutions are, 3i and 3i. 78. By the Zero Product Property: The solutions are and. esolutions Manual - Powered by Cognero Page 14

80. MODELS A model car builder is building a display table for model cars. He wants the perimeter of the table to be 26 feet, but he wants the area of the table to be no more than 30 square feet. What could be the width of the table? Let w and l be the width and the length of the table. The equation and the inequality represent this situation is: Solve the corresponding quadratic equation. Therefore, the solution region of the inequality is. Since w is the width of the table, it can not be negative. Also, the perimeter of the table to be 26 feet; therefore, the width of the table could be between 0 and 3 ft or between 10 and 13 feet. esolutions Manual - Powered by Cognero Page 15

82. FOOD The Hot Dog Grille offers the lunch combinations shown. Assume that the price of a combo meal is the same price as purchasing each item separately. Find the prices for a hot dog, a soda, and a bag of potato chips. Let x, y and z be the price for a hot dog, a soda and a bag of potato chips. The system of equations representing this situation is: Use Cramer s Rule to find the values of x, y, and z. The solutions are (1.95, 1.50, 0.90). The price for a hot dog is $1.95. The price for a soda is $1.50. The price for a bag of potato chips is $0.90. Evaluate each expression. 84. esolutions Manual - Powered by Cognero Page 16

86. 88. esolutions Manual - Powered by Cognero Page 17

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