Recall that when you multiply a number by itself, you square the number. = 16 4 squared is = 4 2 = 4 The square root of 16 is 4.
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1 6.1 Propertie of Square Root How can you multiply and divide quare root? Recall that when you multiply a number by itelf, you quare the number. Symbol for quaring i nd power. = To undo thi, take the quare root of the number. = 16 quared i 16. Symbol for quare root i a radical ign. 16 = = The quare root of 16 i. 1 ACTIVITY: Finding Square Root Work with a partner. Ue a quare root ymbol to write the ide length of the quare. Then find the quare root. Check your anwer by multiplying. a. Sample: = 81 = 9 ft Area 81 ft Check The ide length of the quare i 9 feet. b. Area 11 yd c. Area = cm d. Area = 61 mi COMMON CORE Square Root In thi leon, you will implify and evaluate quare root. implify radical expreion. Preparing for Standard N.RN. e. Area =.89 in. f. Area 6.5 m g. 16 Area ft 5 60 Chapter 6 Exponential Equation and Function
2 ACTIVITY: Operation with Square Root Math Practice Analyze Conjecture How do you know if your concluion i accurate? How can you explain your concluion? Work with a partner. When you have an expreion that involve two operation, you need to know whether you obtain the ame reult regardle of the order in which you perform the operation. In each of the following, compare the reult obtained by the two order. What can you conclude? a. Square Root and Addition I equal to 6 + 6? In general, i a + b equal to a + b? Explain your reaoning. b. Square Root and Multiplication I 9 equal to 9? In general, i a b equal to a b? Explain your reaoning. c. Square Root and Subtraction I 6 6 equal to 6 6? In general, i a b equal to a b? Explain your reaoning. d. Square Root and Diviion I 100 equal to 100? In general, i a b equal to a b? Explain your reaoning.. IN YOUR OWN WORDS How can you multiply and divide quare root? Write a rule for: a. The product of quare root b. The quotient of quare root Ue what you learned about quare root to complete Exercie 5 on page 6. Section 6.1 Propertie of Square Root 61
3 6.1 Leon Leon Tutorial Product Property of Square Root Algebra Number xy = x y, where x, y = 9 5 = 5 Quotient Property of Square Root Algebra Number x y = x y, where x 0 and y > 0 = = Remember EXAMPLE A quare root i implified when the radicand ha no perfect quare factor other than 1. 1 Simplifying Square Root a. 150 = 5 6 Factor uing the greatet perfect quare factor. b = 15 6 = 5 6 Product Property of Square Root = 5 6 Simplify. = 15 8 Quotient Property of Square Root Simplify. EXAMPLE Evaluating Square Root Evaluate b ac when a =, b = 8, and c =. b ac = ( 8) ()() Subtitute. = Simplify. = 16 Factor. = 16 Product Property of Square Root = Simplify. Exercie 6 17 Simplify the expreion Evaluate b ac when a =, b = 6, and c = 5. 6 Chapter 6 Exponential Equation and Function
4 EXAMPLE Simplifying Radical Expreion Simplify = 6 + = 6 + = 6 + Factor the radicand. Product Property of Square Root Simplify. = + Divide. EXAMPLE Real-Life Application a 0 ft b 16 ft The circumference C of the art room in a manion i given by the a formula C = π + b. Find the circumference of the room. C = π a + b Write formula. Dining Guet Entrance Hall Hall Art Guet Living = π Subtitute. = π 8 Simplify. = π 8 Factor. = π 8 Product Property of Square Root = π 8 Simplify. The circumference of the room i π 8, or about 11 feet. Simplify the expreion. Exercie () 8. Ue the formula in Example to find the circumference of an ellipe in which a = 1 feet and b = 6 feet. Section 6.1 Propertie of Square Root 6
5 6.1 Exercie Help with Homework 1. WRITING How do you know when the quare root of a poitive integer i implified?. WRITING How i the Product Property of Square Root imilar to the Quotient Property of Square Root? 9+(-6)= +(-)= +(-9)= 9+(-1)= Find the dimenion of the quare. Check your anwer.. Area 6 ft. Area 1 in Area cm 16 1 Simplify the expreion Evaluate the expreion when x =, y = 8, and z = x + yz 16. x + y 17. y xz 18. ERROR ANALYSIS Decribe and correct the error in implifying the expreion. 0 9 = 0 9 = ELECTRICITY The electric current I (in ampere) an appliance ue i given by the formula I = P, where P i the power (in watt) R and R i the reitance (in ohm). Find the current an appliance ue when the power i 17 watt and the reitance i ohm. 6 Chapter 6 Exponential Equation and Function
6 0. BASEBALL You drop a baeball from a height of 56 feet. Ue the expreion, where h i the height (in feet), to find the time (in econd) it take the 16 baeball to hit the ground. h Simplify the expreion (5) 7. VOLUME A pet tore intall a new aquarium in your teacher claroom. What i the volume of the aquarium? 5 ft 0 7 ft 6 ft 7 8 ft ft 8. BILLBOARD What i the area of the rectangular billboard? Simplify the expreion. Aume all variable are poitive. 9. x y 0. 5y z 1. 18x y z. Modeling Write an equation that repreent the ide length of a cube a a function of the urface area A of the cube. Find the ide length when the urface area i 7 quare feet. Evaluate the expreion. (Skill Review Handbook) MULTIPLE CHOICE Which value i equivalent to 6(0.)? (Skill Review Handbook) A B 0.08 C 1.78 D.6 Section 6.1 Propertie of Square Root 65
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