Assignment 5 unit3-4-radicals. Due: Friday January 13 BEFORE HOMEROOM
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1 Assignment 5 unit3-4-radicals Name: Due: Friday January 13 BEFORE HOMEROOM Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write the prime factorization of Write the prime factorization of Determine the greatest common factor of 280 and 360. a. 9 b. 63 c d Determine the greatest common factor of 84, 210, and 336. a. 14 b c. 21 d Determine the least common multiple of 10 and 22. a. 2 b. 55 c. 220 d Determine the least common multiple of 78 and 102. a b. 6 c d A developer wants to subdivide a rectangular plot of land measuring 600 m by 750 m into congruent square lots. What is the side length of the largest possible square? a. 75 m b. 30 m c. 150 m d. 50 m 8. One neighbour cuts his lawn every 8 days. Another neighbour cuts her lawn every 10 days. Suppose both neighbours cut their lawns today. How many days will pass before both neighbours cut their lawns on the same day again? a. 80 days b. 60 days c. 2 days d. 40 days 9. What is the side length of the largest square that could be used to tile a rectangle that measures 6 ft. by 34 ft.? Assume the squares cannot be cut. a. 6 ft. b. 2 ft. c. 102 ft. d. 4 ft. 10. There are 16 male students and 20 female students in a Grade 10 math class. The teacher wants to divide the class into groups with the same number of males and the same number of females in each group. What is the greatest number of groups the teacher can make? a. 12 b. 4 c. 8 d Determine the cube root of a b c d A cube has volume cm 3. What is the surface area of the cube? a cm 2 b cm 2 c. 25 cm 2 d cm Determine the perfect square whole number closest to a b c d How many perfect square whole numbers are between 5000 and 6000? a. 6 b. 8 c. 1 d How many perfect cube whole numbers are between 6000 and 8500? a. 3 b. 2 c. 1 d Which of the following numbers is not both a perfect square and a perfect cube? a b c d Identify the index of. a. b. 3 c. 7 d Identify the radicand of. a. 4 b. c. 6 d Evaluate. a. 2 b. 2.6 c. 16 d. 1.41
2 20. Evaluate. a. 4 b. impossible c d Evaluate. a. 0.7 b c d Evaluate. 23. Write an equivalent form of 9 as a cube root. 24. Write an equivalent form of as a square root. 25. Which of these roots lies between 3 and 4?,,, 26. Evaluate. a. 0.1 b. 1.3 c. 1.8 d Which of these numbers is rational?,,, 28. Which of these numbers is irrational?,,, 29. For which number will the fourth root be rational? 256, 27, 81, a b. 81 c. 27 d Which of these numbers is an integer, but not a whole number? 9, 0, 1, a. 0 b. 9 c. d Which of these numbers is a natural number? 9, 0, 1, a. 9 b. 0 c. d Which irrational number could be used to represent the hypotenuse of a right triangle with legs 7 cm and 8 cm? a. cm b. cm c. cm d. cm 33. The area of a square is 64 square inches. What do you know about the square? a. Both its side length and its perimeter are irrational. b. Its side length is irrational and its perimeter is rational. c. Its side length is rational and its perimeter is irrational. d. Both its side length and its perimeter are rational.
3 34. To which set(s) of numbers does belong? I II III IV Natural Integer Rational Irrational a. II and III only b. III only c. I, II and III only d. IV only 35. Write in simplest form. a. b. 6 3 c. d. 36. Write in simplest form. 37. Write in simplest form. 38. Write 6 5 as an entire radical. 39. Write as an entire radical. 40. Write as an entire radical. 41. Write in simplest form. a. b. 7 2 c. d. 42. Write in simplest form. 43. Write 7 14 as an entire radical. 44. Write as an entire radical. 45. Evaluate without using a calculator. a. 8 b. 4 c. 4 d Evaluate without using a calculator. a b c. 0.5 d Evaluate without using a calculator. a. 3 b. 3 c. 9 d. does not exist 48. Evaluate without using a calculator. 49. Write as a radical.
4 50. Write as a power. 51. Evaluate a. 27 c. 27 b. does not exist d Biologists use the formula to estimate the brain mass, b kilograms, of a mammal with body mass m kilograms. Estimate the brain mass of a mammal with body mass 276 kg. a. About 4.24 kg c. About 9.13 kg b. About 0.42 kg d. About kg 53. A cube has volume 1200 cubic inches. Write the edge length of the cube as a power. a. in. b. c. in. d. in. in. 54. Evaluate a. c. b.... d. 55. Arrange these numbers in order from greatest to least.,,,, a. b.,,,,,,,, c. d.,,,,,,,, Problem 56. Chris completes one lap of a go-cart track every 40 s. D Arcy completes one lap of the same track every 50 s. Suppose Chris and D Arcy cross the starting line at the same time. How many seconds will pass before they cross the starting line at the same time again? How many laps will Chris have completed in that time? How many laps will D Arcy have completed in that time? (LCM) 57. A cube has surface area 2646 m 2. What is its volume? 58. A square has area 40.0 cm 2. Determine the perimeter of the square to the nearest tenth of a centimetre.
5 59. Calculate the volume of the largest possible sphere that can fit in a cube with volume cm 3. Give the volume to the nearest tenth of a cubic centimetre. Explain your steps. 60. Is the cube root of 250 rational or irrational? Use 2 different strategies to justify your answer. 61. Determine whether the perimeter of a square with area 28 m is a rational number or an irrational number. 62. In isosceles ABC, what is the length of BC? Write your answer as a mixed radical. A 10ft. 5 ft. B D C 63. A formula for the approximate surface area, SA square metres, of a person s body is, where m is the person s mass, in kilograms. Calculate the surface area of a person with mass 75 kg. 64. Another formula for the approximate surface area, SA square metres, of a person s body is, where h is the person s height in centimetres, and m is the person s mass in kilograms. a) Calculate the surface area of a newborn with height cm and mass 7.3 kg. Write the answer as a decimal to the nearest hundredth of a square centimetre. b) Calculate the surface area of a person with height 170 cm and mass 66 kg. Write the answer as a decimal to the nearest hundredth of a square centimetre.
6 65. Here is Tanisha s solution for evaluating a power: Identify the errors Tanisha made. Write a correct solution.
7 assignment 5 unit3-4-radicals Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: Easy 2. ANS: B PTS: 1 DIF: Easy 3. ANS: D PTS: 1 DIF: Easy 4. ANS: D PTS: 1 DIF: Moderate 5. ANS: D PTS: 1 DIF: Easy 6. ANS: A PTS: 1 DIF: Easy 7. ANS: C PTS: 1 DIF: Moderate 8. ANS: D PTS: 1 DIF: Moderate 9. ANS: B PTS: 1 DIF: Moderate 10. ANS: B PTS: 1 DIF: Moderate 11. ANS: D PTS: 1 DIF: Easy REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots 12. ANS: B PTS: 1 DIF: Moderate REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots 13. ANS: B PTS: 1 DIF: Easy REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots 14. ANS: D PTS: 1 DIF: Moderate REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots
8 15. ANS: B PTS: 1 DIF: Moderate REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots 16. ANS: B PTS: 1 DIF: Moderate REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots 17. ANS: B PTS: 1 DIF: Easy REF: 4.1 Estimating Roots LOC: 10.AN2 18. ANS: B PTS: 1 DIF: Easy REF: 4.1 Estimating Roots LOC: 10.AN2 19. ANS: A PTS: 1 DIF: Easy REF: 4.1 Estimating Roots LOC: 10.AN2 20. ANS: A PTS: 1 DIF: Easy REF: 4.1 Estimating Roots LOC: 10.AN2 21. ANS: A PTS: 1 DIF: Easy REF: 4.1 Estimating Roots 22. ANS: A PTS: 1 DIF: Easy REF: 4.1 Estimating Roots LOC: 10.AN2 23. ANS: B PTS: 1 DIF: Easy REF: 4.1 Estimating Roots 24. ANS: D PTS: 1 DIF: Easy REF: 4.1 Estimating Roots 25. ANS: C PTS: 1 DIF: Moderate REF: 4.1 Estimating Roots LOC: 10.AN2 26. ANS: C PTS: 1 DIF: Moderate REF: 4.1 Estimating Roots LOC: 10.AN2 27. ANS: D PTS: 1 DIF: Easy REF: 4.2 Irrational Numbers LOC: 10.AN2 28. ANS: B PTS: 1 DIF: Easy REF: 4.2 Irrational Numbers LOC: 10.AN2 29. ANS: D PTS: 1 DIF: Moderate REF: 4.2 Irrational Numbers LOC: 10.AN2 30. ANS: B PTS: 1 DIF: Easy REF: 4.2 Irrational Numbers LOC: 10.AN2 31. ANS: A PTS: 1 DIF: Easy REF: 4.2 Irrational Numbers LOC: 10.AN2 32. ANS: A PTS: 1 DIF: Easy REF: 4.2 Irrational Numbers 33. ANS: D PTS: 1 DIF: Easy REF: 4.2 Irrational Numbers 34. ANS: A PTS: 1 DIF: Easy REF: 4.2 Irrational Numbers LOC: 10.AN2 35. ANS: B PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals LOC: 10.AN2 36. ANS: B PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals LOC: 10.AN2 37. ANS: A PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals LOC: 10.AN2 38. ANS: C PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals
9 LOC: 10.AN2 39. ANS: A PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals LOC: 10.AN2 40. ANS: C PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals LOC: 10.AN2 41. ANS: B PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals LOC: 10.AN2 42. ANS: D PTS: 1 DIF: Moderate REF: 4.3 Mixed and Entire Radicals LOC: 10.AN2 43. ANS: C PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals LOC: 10.AN2 44. ANS: B PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals LOC: 10.AN2 45. ANS: B PTS: 1 DIF: Easy 46. ANS: C PTS: 1 DIF: Easy 47. ANS: A PTS: 1 DIF: Easy 48. ANS: C PTS: 1 DIF: Easy 49. ANS: B PTS: 1 DIF: Easy 50. ANS: B PTS: 1 DIF: Easy 51. ANS: A PTS: 1 DIF: Moderate 52. ANS: B PTS: 1 DIF: Moderate 53. ANS: B PTS: 1 DIF: Easy 54. ANS: C PTS: 1 DIF: Moderate 55. ANS: B PTS: 1 DIF: Moderate PROBLEM
10 56. ANS: The time, in seconds, that will pass is the least common multiple of 40 and 50. List the multiples of each number until the same multiple appears in both lists. Multiples of 40 are: 40, 80, 120, 160, 200,... Multiples of 50 are: 50, 100, 150, 200,... The least common multiple of 40 and 50 is 200. So 200 s will pass before Chris and D Arcy cross the starting line at the same time again. It takes 40 s for Chris to complete one lap. So, in 200 s, Chris will complete It takes 50 s for D Arcy to complete one lap. So, in 200 s, D Arcy will complete 5 laps. 4 laps. PTS: 1 DIF: Moderate KEY: Problem-Solving Skills 57. ANS: To calculate the volume, first determine the edge length of the cube. The surface area of a cube is the sum of the areas of its 6 congruent square faces. So, the area, A, of one face is: The edge length, e, of the cube is the square root of the area of one square face. So, the volume, V, of the cube is the cube of its edge length. The volume of the cube is 9261 m 3. PTS: 1 DIF: Easy REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots KEY: Problem-Solving Skills 58. ANS: To calculate the perimeter, first determine the side length of the square. The side length, s, of a square is equal to the square root of its area.... The perimeter, P, of a square is 4 times its side length.
11 The perimeter of the square is approximately 25.3 cm. PTS: 1 DIF: Moderate REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots KEY: Problem-Solving Skills 59. ANS: To determine the volume of the sphere, first determine the edge length of the cube. The edge length, e, of a cube is equal to the cube root of its volume. The radius, r, of the largest sphere that will fit in the cube is one-half of the edge length of the cube. Use the formula for the volume of a sphere. he volume of the largest possible sphere that can fit in the cube is approximately cm 3. PTS: 1 DIF: Difficult REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots KEY: Communication Problem-Solving Skills 60. ANS: 250 is not a perfect cube, so the cube root of 250 is irrational. = So, the cube root of 250 is likely irrational. PTS: 1 DIF: Moderate REF: 4.2 Irrational Numbers KEY: Problem-Solving Skills 61. ANS: The formula for the area, A, of a square with side length s units is: To determine the value of s, take the square root of each side.
12 Since 28 is not a perfect square, is irrational. So, the side length of the square is irrational. The perimeter of a square is: P = 4s Since the product of 4 and an irrational number is irrational, the perimeter of the square is irrational. PTS: 1 DIF: Difficult REF: 4.2 Irrational Numbers LOC: 10.AN2 KEY: Problem-Solving Skills 62. ANS: Use the Pythagorean Theorem in ABD to determine BD. So, The length of BC is ft. PTS: 1 DIF: Moderate REF: 4.3 Mixed and Entire Radicals LOC: 10.AN2 KEY: Problem-Solving Skills 63. ANS: Substitute m = 75 in the formula:... The surface area of a person with mass 75 kg is approximately 2.0 m 2. PTS: 1 DIF: Moderate KEY: Problem-Solving Skills 64. ANS: Use the formula: a) Substitute: h = 48 and m = 7.3
13 Use a calculator. The surface area of a newborn with height cm and mass 7.3 kg is approximately 0.32 cm. b) Substitute: h = 170 and m = 66 Use a calculator. The surface area of a person with height 170 cm and mass 66 kg is approximately 1.58 cm. PTS: 1 DIF: Moderate KEY: Problem-Solving Skills 65. ANS: Tanisha made an error in the first line when she wrote the square root symbol ( ) instead of the ( ) symbol. Also, the exponent outside the bracket should have been 2, not 7. (The numerator of a fractional exponent represents the index of the radical and the denominator represents the exponent of the power.) A correct solution: PTS: 1 DIF: Moderate KEY: Problem-Solving Skills Communication
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