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Name: ______________________ Class: __________________ AU8: Notes #3 – Cube Roots Date: __________________ Warm-up: Chloe wants to build a storage container in the shape of a cube to hold 125 cubic meters of hay for her horse. Find the length of one side of the container. Vocabulary: When you use a number as a factor three times, you are cubing that number or raising it to the third power. For example: 4 3 64 . Numbers whose cube roots are integers or quotients of integers are called perfect cubes. Let’s list some other perfect cubes that you know. x 1 2 3 4 5 6 7 8 9 10 64 125 216 343 512 729 1,000 x3 Let’s look at the inverse of cubing: n 3 1 8 27 n Every number (positive, negative, or zero) have exactly one cube root. Solve the following equations: r3 8 x 3 125 1 Example A: Evaluate the following cube roots or solve the equations. 1. 3 729 2. x 3 1000 3. 3 512 4. x 3 216 5. 3 8 64 6. 3 0.125 Special Cases: Negative Cube Roots Solve the following and explain: r 3 8 x 3 125 Evaluate the following: 3 729 3 2 512 Real-World Problems: The volume of a Rubik’s cube is 216 cm3, what is the length of one of its sides? Find the radius of a spherical globe with a volume of 288π in3. Try It! a. Find the volume of a cube if the side length is 4 feet. b. Dylan has a planter in the shape of a cube that holds 8 cubic feet of potting soil. Solve the equation 8 s 3 to find the side length s of the container. 3