4. Finding Cube Root How i the cube root of a number different from the quare root of a number? When you multiply a number by itelf twice, you cube the number. Symbol for cubing i the exponent. 4 = 4 4 4 = 64 4 cubed i 64. To undo thi, take the cube root of the number. Symbol for cube root i. 64 = 4 = 4 The cube root of 64 i 4. ACTIVITY: Finding Cube Root Work with a partner. Ue a cube root ymbol to write the edge length of the cube. Then find the cube root. Check your anwer by multiplying. a. Sample: = 4 = 7 = 7 inche Volume 4 in. Check 7 7 7 = 49 7 = 4 The edge length of the cube i 7 inche. b. Volume 7 ft c. Volume 5 m Cube Root In thi leon, you will find cube root of perfect cube. evaluate expreion involving cube root. ue cube root to olve equation. d. Volume 0.00 cm e. Volume yd 8 6 Chapter 4 Real Number and the Pythagorean Theorem
Math Practice View a Component When writing the prime factorization in Activity, how many time do you expect to ee each factor? Why? ACTIVITY: Uing Prime Factorization to Find Cube Root Work with a partner. Write the prime factorization of each number. Then ue the prime factorization to find the cube root of the number. a. 6 6 7 8 9 4 6 = Prime factorization = ( ) ( ) ( ) Commutative Property of Multiplication = Simplify. The cube root of 6 i. b. 000 c. 75 d. STRUCTURE Doe thi procedure work for every number? Explain why or why not.. Complete each tatement uing poitive or negative. a. A poitive number time a poitive number i a number. b. A negative number time a negative number i a number. c. A poitive number multiplied by itelf twice i a number. d. A negative number multiplied by itelf twice i a number. 4. REASONING Can a negative number have a cube root? Give an example to upport your explanation. 5. IN YOUR OWN WORDS How i the cube root of a number different from the quare root of a number? 6. Give an example of a number whoe quare root and cube root are equal. 7. A cube ha a volume of,84 cubic meter. Ue a calculator to find the edge length. Ue what you learned about cube root to complete Exercie 5 on page 66. Section 4. Finding Cube Root 6
4. Leon Leon Tutorial Key Vocabulary cube root, p. 64 perfect cube, p. 64 A cube root of a number i a number that, when multiplied by itelf, and then multiplied by itelf again, equal the given number. A perfect cube i a number that can be written a the cube of an integer. The ymbol i ued to repreent a cube root. EXAMPLE Finding Cube Root Find each cube root. a. 8 Becaue = 8, 8 = =. b. 7 c. 64 Becaue ( ) = 7, 7 = ( ) =. Becaue ( 4) = 64, ( 64 = 4) = Cubing a number and finding a cube root are invere operation. You can ue thi relationhip to evaluate expreion and olve equation involving cube. 4. EXAMPLE Evaluating Expreion Involving Cube Root Evaluate each expreion. a. 6 = ( 6) Evaluate the cube root. = Multiply. = 5 Subtract. b. ( 5 ) + = 5 + Evaluate the power uing invere operation. = 46 Add. Exercie 6 7 Find the cube root... Evaluate the expreion. 7 4. 000 4. 8 4 8 5. ( 64 ) + 4 6. 5 5 9 64 Chapter 4 Real Number and the Pythagorean Theorem
EXAMPLE Evaluating an Algebraic Expreion Evaluate x 4 + x when x = 9. x 4 + x = 9 4 + 9 Subtitute 9 for x. = 48 + 64 Simplify. = 48 + 4 Evaluate the cube root. = 5 Add. Exercie 8 0 Evaluate the expreion for the given value of the variable. 7. 8y + y, y = 64 8. b 9b, b = EXAMPLE 4 Real-Life Application Remember The volume V of a cube with edge length i given by V =. The urface area S i given by S = 6. Find the urface area of the baeball diplay cae. The baeball diplay cae i in the hape of a cube. Ue the formula for the volume of a cube to find the edge length. V = Write formula for volume. 5 = Subtitute 5 for V. 5 = 5 = Simplify. Take the cube root of each ide. Volume 5 in. The edge length i 5 inche. Ue a formula to find the urface area of the cube. S = 6 Write formula for urface area. = 6(5) Subtitute 5 for. = 50 Simplify. So, the urface area of the baeball diplay cae i 50 quare inche. 9. The volume of a muic box that i haped like a cube i 5 cubic centimeter. Find the urface area of the muic box. Section 4. Finding Cube Root 65
4. Exercie Help with Homework. VOCABULARY I 5 a perfect cube? Explain.. REASONING Can the cube of an integer be a negative number? Explain. 9+(-6)= +(-)= 4+(-9)= 9+(-)= Find the edge length of the cube.. Volume 5,000 in. 4. Volume ft 7 5. Volume 0.064 m Find the cube root. 6. 79 7. 5 8. 000 9. 78 0. 4. 5 64 Evaluate the expreion.. 8 ( 7 ). ( 8 ) + 4 5. 4 6 4. 5 79 4 6. 54 + 4096 7. 4 8000 6 Evaluate the expreion for the given value of the variable. 8. n 4 + n 0, n = 500 9. 6w w, w = 88 0. d + 45d, d = 75. STORAGE CUBE The volume of a platic torage cube i 7,000 cubic centimeter. What i the edge length of the torage cube?. ICE SCULPTURE The volume of a cube of ice for an ice culpture i 64,000 cubic inche. a. What i the edge length of the cube of ice? b. What i the urface area of the cube of ice? 66 Chapter 4 Real Number and the Pythagorean Theorem
Copy and complete the tatement with <, >, or =.. 4 8 5 6. DRAG RACE The etimated velocity v (in mile per hour) of a car at the end of a drag race i v = 4 p, where p i the horepower of the w car and w i the weight (in pound) of the car. A car ha a horepower of and weigh 744 pound. Find the velocity of the car at the end of a drag race. Round your anwer to the nearet whole number. 4. 0.00 0.0 5. 64 64 7. NUMBER SENSE There are three number that are their own cube root. What are the number? 8. LOGIC Each tatement below i true for quare root. Determine whether the tatement i alo true for cube root. Explain your reaoning and give an example to upport your explanation. a. You cannot find the quare root of a negative number. b. Every poitive number ha a poitive quare root and a negative quare root. 9. GEOMETRY The pyramid ha a volume of 97 cubic inche. What are the dimenion of the pyramid? 0. RATIOS The ratio 5 : x i equivalent to the ratio x : 5. What i the value of x? Solve the equation. x in. x in. x in.. (x + 4) = 97. ( 8x 9 ) = 58. ( (5x 6) 4 ) = 6,000 Evaluate the expreion. (Skill Review Handbook) 4. + 4 5. 8 + 5 6. 5 7. 5 4 8. MULTIPLE CHOICE Which linear equation i hown by the table? (Section.6) x 0 y 4 7 0 A y = x + B y = 4x C y = x + D y = 4 x Section 4. Finding Cube Root 67