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CC-11 Cube Roots A cube number is a power with an exponent of 3. The cube of a whole number is a perfect cube. 3 ∙ 3 ∙ 3 5 33 5 27. 8.EE.2 Use … cube root symbols to represent solutions to equations of the form … x3 5 p, where p is a positive rational number. Evaluate … cube roots of small perfect cubes … Test Prep Tip Volume is measured in cubic units. Area is measured in square units. Length is measured in linear units. You can work backward from a perfect cube, such as 27, to find the number 3. This is called a cube root. The cube root of a number is another number that, when raised to the third power, is equal to the given number. The number 3 is the cube root of 27. 3 3 3 3 The symbol " means the cube root of a number. 3 3 3 " 27 5 " 3 5 3. Finding Cube Roots A cube-shaped packing box has a volume of 64 cubic feet. What is the side length of the box? The formula for the volume V of a cube is V 5 s3 , where s is the length of one side. 3 So, the length of one side s is " V , the cube root of the volume V. 3 3 s5" V5" 64 5 4 The side length of the box is 4 feet. Think: 64 5 4 ∙ 4 ∙ 4 64 ft3 1. Find each cube root. a. 3 " 125 b. 3 " 1 c. 3 " 512 You can find cube roots by solving equations of the form x3 = p. To find the cube root of a fraction, find the cube root of the numerator and the cube root of the denominator. Use after Lesson 11-1. CC28 CC-11 Cube Roots 3 1 Å27 3 5 "1 3 "27 5 13 Solving Cube Root Equations Test Prep Tip One way to find a cube root is to guess a number and raise it to the third power. The cube of an even number will always be even and the cube of an odd number will always be odd. 1 Solve x3 5 8 . x3 5 18 d Write the equation. 3 3 " x 5 3Å18 d Take the cube root of each side. 3 "1 5 d Rewrite the cube root of the fraction. 3 "8 x 5 12 d Simplify. Think: 1 5 1 ∙ 1 ∙ 1 and 8 5 2 ∙ 2 ∙ 2. 2. Solve each equation. 8 1 b. x3 5 27 a. x 3 5 2 1 6 c. x3 5 343 Homework Exercises Find the side length of a cube with each given volume. For Exercises See Examples 1–9 1 10–15 2 1. 1,000 m3 2. 1 cm3 3. 729 ft3 Find each cube root. 3 3 4. "216 3 5. "8 3 6. "64 3 7. "27 3 343 9. " 8. "512 Solve each equation. 10. x3 5 125 1 11. x3 5 729 27 12. x3 5 216 512 13. x3 5 125 343 14. x3 5 729 15. x3 5 1,000 16. Guided Problem Solving Find the cube root of 0.008. • Can you rename the decimal as a fraction? • Write your answer as a decimal. Check by cubing your answer. 17. Find the cube root of 0.216. 18. Writing in Math Is 0.3 the cube root of 0.27? Explain. 19 a. Copy and complete the table below. x 1 2 3 4 5 6 7 8 9 10 x2 x3 b. Are any of the numbers both a perfect square and a perfect cube? c. When x is a perfect square, what is true about the cube of x? CC-11 Cube Roots CC29