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Square Roots and Cube Roots Unit 1 © Curriculum Associates, LLC Copying Is Not Permitted © Practice and Problem Solving Curriculum Associates,LLC Practice Lesson 2 Square Roots and Cube Roots Cube and Roots 2Square Lesson Practice Lesson 2 Square Roots and Cube Roots Name: Solve. Copying is notpermitted. B 4 Alberto is saving money to buy a pair of shoes that cost Prerequisite: Understand Solutions to Equations $58. He has already saved $32. He still needs to save d dollars. Study the example problem showing how to write and solve an equation. Then solve problems 1–7. a. Write an equation so that one side of the equation represents the cost of the shoes. Example 32 1 d 5 58 Isabella has filled 3 album pages with photos. Each page has the same number of photos. Isabella has 24 photos. Write b. Explain how to solve your equation to fi nd how and solve an equation to find how many photos are on one much more money Alberto needs to save. How album page. much more does he need to save? Choose a variable to represent the p I must find the amount that when added to 32 gives me 58. Because 32 1 26 5 58, number of photos on one page. I know Alberto needs to save another $26. Write an expression to describe the 3p total number of photos on the pages. Write an equation to compare the 3p 5 24 expression and the number of photos M 5 The bar model illustrates a division equation. What is the Isabella has. equation? Explain how you know. Draw a bar model to represent 24 s Unit 1Expressions and Equations (Exponents) and the Number System You multiply 3 the equation. 8 8 8 8 8 p p p by 8 to get 24. There are 8 photos on one album page. s 4 5 5 8; The model shows a quantity s divided into 5 equal parts, and each part equals 8. B 1 What does the variable p represent in the example 6 5 5 problem? M In the equation 10n 120, is n 10? How do you know? No; Possible explanation: If n 5 10, the expression 10n equals 100, not 120. The variable p represents the number of photos on each page of the album. 7 B 2 What is the solution to the equation 3p 5 24? C Write an equation that has a solution of 7, includes a variable, and uses multiplication. Write a real-world p equals 8. problem that you could represent with your equation. Vocabulary Show how you know that 7 is the solution. M 3 Then Isabella fi lled 3 more pages with 36 photos which Possible answer: 6x 5 42; Erika buys 6 movie tickets. The total cost of the tickets is $42. she evenly divided between the pages. Is the number of equation a statement that tells you two photos on one of these pages more or less than the What is the cost of each movie ticket? $7 is the solution because 6 ? $7 5 $42. number on one page in the example problem? Explain. expressions are equivalent. more than; Possible explanation: 36 > 24, so there 4 1 5 5 9 2b 5 14 would be more than 8 photos on each album page. ©Curriculum Associates, LLC Copying is not permitted. Lesson 2 Square Roots and Cube Roots 1313 1414 Lesson 2 Square Roots and Cube Roots ©Curriculum Associates, LLC Copying is not permitted. Unit 1 Key 5 B Basic M Medium C Challenge 6 Practice and Problem Solving Practice Lesson 2 Square Roots and Cube Roots Cube and Roots 2Square Lesson Practice Lesson 2 Name: Solve. Find Cube Roots M 5 You can use prime factorization to fi nd a cube root. Study the example problem showing how to find a cube root. Then solve problems 1–8. a. Complete the prime factorization of 64. 64 Example Each edge of a cube is x centimeters long. The volume of the 8 8 cube is 343 cm3. What is the length of each edge of the cube? Use the formula for the volume of a cube. 2 4 2 4 3 x 5 V Write the formula. x x3 5 343 Substitute x for b and 343 for V. 22 2 22 2 3 x 5 Ï ····343 Find the cube root of 343. x b. Show the prime factors as 3 equal groups of 2 factors. x 3 2? 2 2? 2 2? 2 x 5 7 Simplify. Volume 5 343 cm ( ) ( ) ( ) 3 4 Each edge of the cube is 7 centimeters long. c. What is Ï ···64 ? M 6 Is 48 a perfect cube? Explain your reasoning. B 1 What is the relationship of the volume of the cube to its No; Possible explanation: The prime factorization of 48 is 2 • 2 • 2 • 2 • 3. I cannot make edge length? 3 equal groups of factors. The volume is the cube of the length of an edge. M 7 Explain how a cube root is diff erent from a square root. B 2 What is the relationship of the edge length of the cube Unit 1Expressions and Equations (Exponents) and the Number System to its volume? Possible explanation: A cube root is a number multiplied together three times to get the The length of an edge is the cube root of the Vocabulary original number. A square root is a number multiplied by itself to get the original number. cube root any number © volume. that is multiplied 8 The volume of Cube A is 216 cubic inches. The length of each edge in Cube B is 2 inches longer Curriculum Associates,LLC C together three times to than the length of each edge in Cube A. How much greater is the volume of Cube B than the M 3 The volume of a cube is 8 ft3. What is the length of each get the original number. volume of Cube A? edge of the cube? 3 ··8 5 2 Show your work. Each edge of the cube is 2 feet long. Ï 3 2 is the cube root of 8. length of edge of Cube A: Ï ····216 5 6, or 6 in.; M 4 Explain the diff erence between a number that is a cube perfect cube the length of edge of Cube B: 2 in. 1 6 in. 5 8 in. and a number that is a cube root. product of an integer Cube B volume: 83 5 512, or 512 in.3 multiplied together Possible explanation: A cube is the product of 3 3 3 three times. 512 in. 2 216 in. 5 296 in. three identical factors. A cube root is the factor 33 5 27 The volume of Cube B is 296 cubic inches greater than the volume of Cube A. that is used three times to get a cube. 27 is a perfect cube. Solution: Copying is notpermitted. ©Curriculum Associates, LLC Copying is not permitted. Lesson 2 Square Roots and Cube Roots 1515 1616 Lesson 2 Square Roots and Cube Roots ©Curriculum Associates, LLC Copying is not permitted. Unit 1 © Practice and Problem Solving Curriculum Associates,LLC Practice Lesson 2 Square Roots and Cube Roots Cube and Roots 2Square Lesson Practice Lesson 2 Name: Solve. Solve Word Problems Copying is notpermitted. M 4 The distance d in feet that a dropped object falls in Study the example problem showing how to use square t seconds is given by the equation d 4 16 5 t2. How long roots and cube roots to solve word problems. Then solve does it take a dropped object to fall 64 feet? problems 1–6. Show your work. 5 2 Example d ÷ 16 t 5 2 Markus walked halfway around a square park that has an area 64 ÷ 16 t of 90,000 square meters. How many meters did Markus walk? 4 5 t2 Use the formula for the area of a square to find the length of Ï ··4 5 t one side. Markus walked halfway around, so find the total length of two sides of the park to find the distance he walked. 2 5 t s2 5 A Write the formula. Solution: The object takes 2 seconds to fall 64 feet. s2 5 90,000 Substitute 90,000 for A. M 5 The area of the top face of a cube is 9 square centimeters. Use 9 of these cubes to make a rectangular prism. What s 5 Ï ······90,000 Find the square root of 90,000. is the volume of the rectangular prism? s 5 300 The length of each side is 300 m. Show your work. 2 s 5 9; s 5 ··9 5 3, so the length of each side is 3 cm; Unit 1Expressions and Equations (Exponents) and the Number System The length of 2 sides 5 300 • 2 5 600 Ï V 5 33, V 5 27 cm3; 9 • 27 5 243, or 243 cm3 Markus walked 600 meters. Solution: The volume of the rectangular prism is 243 cubic centimeters. B 1 A smaller square park has an area of 3,600 square meters. What is the length of one side of the park? C 6 The diagram shows the dimensions of Taylor’s deck. The x 60 meters area of the deck is 233 square feet. Taylor is going to put a railing along the longest edge. How many feet of 8 ft x 2 When completely full, a cube-shaped container will hold railing will she need? B 8 ft 8,000 cubic centimeters of water. What is the length of Show your work.
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