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Name:__________________________________ th 8 Grade Math 5.2 Homework: Squares, Cubes and Irrational Numbers Period: ____ Squares and Square Roots When you multiply a number by itself, you square the number. 32 = 3 β 3 = 9 To “undo” this, take the square root of the number. (The square root symbol,√ radical.) √9 = √32 = 3 , is called a 1-18 The squares of whole numbers are called perfect squares. Write the first 10 perfect squares. MEMORIZE THEM!! Then write the square roots of these numbers. 12 = 1 β 1 = 1 62 = ____________ √1 = √12 = 1 √36 = ____________ 22 = ____________ 72 = ____________ √4 =____________ √49 = ____________ 32 = ____________ 82 = ____________ √9 = ____________ √64 = ____________ 42 = ____________ 92 = ____________ √16 = ___________ √81 = ____________ √25 = ___________ √144 = ___________ 52 = ____________ 102 = ___________ Area of Squares and Side Lengths The area of a square is the space inside the square. Area is measured in square units. The area of a square can be found by squaring its side. (π΄ = π 2 ) The length of the side of a square can be found by taking the square root of its Area. (π = √π΄) π΄ = 32 = 9 cm2 π = √9 = 3 cm 3 cm 3 cm Use a square root symbol to write the side length of the square. Then find the side length. Round to the nearest tenth. 19. π΄ = 625 in2 20. π΄ = 33.64 ft2 22. Solve. Write your answer in the most accurate form. a. π₯ 2 = 144 b. π₯ 2 = 3 21. π΄ = 342.25 cm2 c. π₯ 2 = 11 Cube Roots and Cubes When you multiply a number by itself three times, you cube the number. 53 = 5 β 5 β 5 = 125 To “undo” this, take the cube root of the number. 3 3 √125 = √53 = 5 23-30 The cubes of whole numbers are called perfect cubes. Write the first 5 perfect cubes. MEMORIZE THEM!! Then write the cube roots of these numbers. 13 = 1 β 1 β 1 = 1 3 23 = ________________________ 3 33 = ________________________ 3 43 = ________________________ 3 53 = ________________________ 3 3 √1 = √13 = 1 √8 = _________________________ √27 = ________________________ √64 = ________________________ √125 = _______________________ Volume of Cubes and Edge Lengths The Volume of a cube is the 3-dimensional space inside the cube. Volume is measured in cubic units. The volume of a cube can be found by cubing its edge. (π = π 3 ) 3 The length of the edge of a cube can be found by taking the cube root of its volume. (π = √π ) 3 cm π = 32 = 27 cm3 3 π = √27 = 3 cm 3 cm 3 cm Use a cube root symbol to write the edge length of the cube. Then find the edge length. Round to the nearest tenth 31. π = 512 in3 33. Solve. Write your answer in the most accurate form. a. π₯ 3 = 729 b. π₯ 3 = 7 32. π = 5832 cm3 c. π₯ 3 = 216 Use your calculator to determine if the following numbers are PERFECT SQUARES (yes/no) 34. 100 _______ 35. 144 _______ 36. 150 _______ 37. 200 ________ 38. 169 _______ 39. 300 _______ 40. 225 _______ 41. 625 ________ Place the following numbers on the number line (make sure to label the point). 42. √8 43. √36 44. −√4 45. √27 46. √20 47. √30 48. √15 49. −√10 3 3 3 Approximate Irrational Square Roots (determine which 2 integers the square root is in between). 50. √5 is in between _____ & ______ 51. √10 is in between _____ & ______ 52. √2 is in between _____ & ______ 53. √12 is in between _____ & ______ Approximate Irrational Cube Roots (determine which 2 integers the cube root is in between). 8 27 64 54. β45 is in between _____ & ______ 55. β5 is in between _____ & ______ 56. β18 is in between _____ & ______ 57. β10 is in between _____ & ______ 58. The following irrational numbers are between what two integers? No calculators. Show your reasoning by showing your work. It might be helpful to make list of the perfect squares/cubes and their roots. Review 59. Convert the following terminating decimals to fractions. Always reduce to lowest terms. 60. Convert the following repeating decimals to fractions. Always reduce to lowest terms. 5.2 KEY 1. 4 3. 16 5. 36 7. 64 9. 100 11. 3 13. 5 15. 7 17. 9 19. 25 in. 21. 18.5 cm 23. 8 25. 64 27. 2 29. 4 31. 8 in. 33. a. 9 35. yes 37. no 39. no 41. yes 43. 6 45. 3 47. 3.107 49. -3.162 51. 3 & 4 53. 3 & 4 55. 1 & 2 57. 2 & 3 59. a. 233/1000