Mini-Lecture 7.1 Radicals and Radical Functions

Mini-Lecture 7. Radicals and Radical Functions Learning Objectives:. Find square roots.. Approimate roots.. Find cube roots.. Find n th roots.. Find n a n when a is an real number. 6. Graph square and cube root functions. 7. Ke vocabular: principal square root, negative square root, inde, n th root. Eamples:. Find each square root. Assume that all variables represent non-negative real numbers. a) b) e) f) 9 g) c) 0.0 d) 9 0 6 h). Approimate each square root to three decimal places. a) b) 7 c) d) 0. Find cube root. Assume that all variables represent non-negative real numbers 6 00 a) 8 b) 6 c) 6 d) 9 6. Find the n th roots.. a) 6 b) 8 c) 8 d) 0 e) 6 f) g) 8 6. Simplif. Assume that the variables represent an real number. a) ( 6) b) ( 7) c) 6 d) ( ) 6. If f( ) = +, solve as indicated a) Find f (0) b) Find f ( 8) c) Find domain d) Graph f ( ) Teaching Notes: Some students think =+ or. Be sure to define principal square root earl. Some students find higher-order radicals confusing at first. Man students are unsure when the absolute value smbol is needed in objective. Refer students to the Finding n a n chart in the tet. Answers: (graph answers at end of mini-lectures) a), b), c) 0., d) -7, e), f), g), h) -0 8 ; a).7, b) 6.08, c) 0.60, d).8; a), b), c), d) -, a), b) -, c) not a real number, d), e), f) ; a) 6, b) -7, c), d) - ; 6a), b) 0, c) all real numbers M-9 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Learning Objectives:. Understand the meaning of. Understand the meaning of a n m n a. m Mini-Lecture 7. Rational Eponents. Understand the meaning of a n.. Use rules for eponents to simplif epressions that contain rational eponents.. Use rational eponents to simplif radical epressions. Eamples:. Use radical notation to rewrite each epression. Simplif if possible. a) b) 8 c) d) 9. Simplif if possible. Write final answers with positive eponents. ) ( 8) e) 6 (6 ) a) 8 b) ( 8) c) ( d) ( 6). Simplif if possible. Write final answers with positive eponents. a) 8 b) ( 6) c) d) 9. Use the properties of eponents to simplif each epression. Write with positive eponents. a) e) b) a a a f) c) 0 ( ) g) 0 0 d) h) 8 ( a b ) ( a b) 8. Use rational eponents to simplif each radical. Assume that all variables represent positive real numbers. a) a b) c) 6 d) Use rational eponents to write as a single radical epression. e) 8 f) g) 9 6 6 ab h) Teaching Notes: Most students think rational eponents are eas once the see that the denominator is the root and the numerator is the power. Refer students to the Definition of n n m a / a / a n and Summar of Eponent Rules charts in tet. Answers: a) =, b) 8 =, c) =, d) 6 8 =, e) 6 =, a) 7, b), c) ; d) -6; a) 9 7, b) 6, c), d) 9 ; a), b) ab, e) 6, f) 7, g), h) 8, c), d) 7, e) a, f), g) 8, h) b a 7 8 ; a) a, b), c), d) Copright 009 Pearson Education, M-0 Inc., publishing as Pearson Prentice Hall

Learning Objectives: Mini-Lecture 7. Simplifing Radical Epressions. Use the product rule for radicals.. Use the quotient rule for radicals.. Simplif radicals.. Use the distance and midpoint formulas. Eamples:. Use the product rule to multipl. Assume that all variables represent positive real numbers. a) b) 7 9 c) d). Use the quotient rule to simplif. Assume that all variables represent positive real numbers. a) 9 6 b) 6 c) 8 9 d) 8 e) 9. Simplif. Assume that all variables represent positive real numbers. a) 0 b) 8 c) 6 d) 6 e) 7 8 90 f) g) h) 8 0 i) 0 j) 80 k) 8 l) 7 m) 9 0 n) 0 o) 9 79 7. Find the distance between each pair of points. a) ( ) ( ) (, 7) ; (, ), ;, 6 b) M- c) (, ) ; ( 7, ) Find the midpoint of each line segment whose endpoints are given. d) (, ) ; (, ) e), ;,, Teaching Notes: f) ( ) ; (, ) Some students have trouble simplifing roots with non-perfect squares inside. Encourage them to write numbers as the product of the highest possible perfect square with another number. Some students need a lot of practice simplifing radicals with no variables before attempting those with variables. Remind students that the root divides the eponent for variables within radicals. Refer students to the Product / Quotient Rules, Distance Formula, and Midpoint Formula charts. Answers: a) 0, b) 6, c), d) 0 ; a) 8, b), c) d), e) 0, f), g), h), i), d) 6 o) ; a) units, b) 6.708 units, c) 9 units, d) (, 7 ), e) ( 9,-), f) 8, e) ; a), b), c),, j), k), l), m), n) 7 7, Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall,

Mini-Lecture 7. Adding, Subtracting, and Multipling Radical Epressions Learning Objectives:. Add or subtract radical epressions.. Multipl radical epressions.. Ke vocabular: like radicals. Eamples:. Add or subtract as indicated. Assume that all variables represent positive real numbers. a) 6 7 b) 00 8 + 9 98 c) 00 d) 8 7 e) 0 7 + 8 f) + g) + h) 00 7 0 i) 0 +. Multipl. Then simplif if possible. Assume that all variables represent positive real numbers. a) 6 ( + 7) b) 7 ( + 7) c) ( 7 ) d) ( ) e) ( 6 + z)( ) f) ( + ) ( + ) g) ( + 9) ( 6 ) h) ( + ) i) ( + 7) ( 7 + ) Teaching Notes: Most students find objective eas once the realize that adding / subtracting like radicals is analogous to adding / subtracting like terms. Some students are not sure how to handle a coefficient in front of a radical once the radical is simplified. Man students distribute the eponent in eamples c) and h). Answers: a) 7, b), c) 8, d), e) 7, f) 9, g), h) 8, i) ; a) 0 +, b) 77 + 7, c) 9, d), e) 8 + (z 6) z, f) + 7 + 0, g) +, h) + + 6, i) 6 7 + 9 9 + Copright 009 Pearson Education, M- Inc., publishing as Pearson Prentice Hall

Learning Objectives: Mini-Lecture 7. Rationalizing Denominators and Numerators of Radical Epressions. Rationalize denominators having one term.. Rationalize denominators having two terms.. Rationalize numerators.. Ke vocabular: rationalize, conjugate. Eamples:. Rationalize each denominator. Assume that all variables represent positive real numbers. a) b) 7 c) 6 d) 8 e) 7 f) a b g) 0 h) 8 9 9. Rationalize each denominator. Assume that all variables represent positive real numbers. a) b) 6 + c) + + d). Rationalize each numerator. Assume that all variables represent positive real numbers. a) b) 8 7 c) 6 d) 6 z e) + f) g) + h) + Teaching Notes: Some students need to see a few eamples of wh a a = a before appling it to rationalizing a denominator. Most students can rationalize denominators easil for square roots. Some students have trouble figuring out what to multipl b when rationalizing higher roots and need a step-b-step procedure. Answers: a), b) 7 7, c), d), e) 6 b) f) 7, f) M- 6ab, g) b 6 + 8 9 + 6, c) 6 +, d) ; a) 9 9 ( + ), g) + +, h) 6, h) 9 0, b), c) 6 80 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall ( + ) ; a), 7, d) z, e) 6,

Mini-Lecture 7.6 Radical Equations and Problem Solving Learning Objectives:. Solve equations that contain radical epressions.. Use the Pthagorean Theorem to model problems.. Ke vocabular: etraneous solution. Eamples:. Solve. Check our solutions. a) = b) + = 7 c) = 6 d) + 6 + =8 e) 6 = f) + = 0 Solve. Check our solutions. g) + = + h) + 0 = i) + = + j) = +6 k) + = l) 7 = + 8. Solve. a) Triangle A triangle has sides of length m and 6m. Find the length of the hpotenuse. b) Triangle A triangle has a hpotenuse of length cm and one leg of length cm. Find the length of the other leg. c) Kite A kite is secured to a rope that is tied to the ground. A breeze blows the kite so that the rope is taught while the kite is directl above a flagpole that is 0ft from where the rope is staked down. Find the altitude of the kite if the rope is 0ft long. d) Voltage The maimum number of volts, E, that can be placed across a resistor is given b E = PR, where P is the power in watts and R is resistance in ohms. If a watt resistor can have at most 0 volts of electricit across it, find the number of ohms of resistance of this resistor. Teaching Notes: Show students a simple eample of an etraneous solution, such as: = = 9 =± = is etraneous. Some students have a lot of trouble with objective. Encourage students to draw a diagram whenever possible for applied problems. Refer students to the Power Rule, Solving a Radical Equation, and Pthagorean Theorem charts in the tet. Answers: a) {}, b) {8}, c), d) {6}, e), f) {0}, g) {6,}, h) {}, i) {}, j) {}, k), l) b) 0 cm, c) 0.8 ft, d) 800 ohms of resistance ; a) 0 m Copright 009 Pearson Education, M- Inc., publishing as Pearson Prentice Hall

Mini-Lecture 7.7 Comple Numbers Learning Objectives:. Write square roots of negative numbers in the form bi. Add or subtract comple numbers.. Multipl comple numbers.. Divide comple numbers.. Raise i to powers. 6. Ke vocabular: imaginar number, comple number, comple conjugate. Eamples:. Write using i notation. a) 9 b) 8 c) d) 0 Write using i notation. Then multipl or divide as indicated. e) 7 f) g) 6 h) 8 6. Add or subtract as indicated. Write our answers in a+ biform. a) ( i) + ( + i) b) ( 8 i) ( i) c) 7 ( 9+ i ). Multipl. Write our answers in a+ biform. a) 6 i 8i b) i i + + e) ( i) ( i) d) ( i) ( i) c) i ( 9i) + f) ( ) i. Divide. Write our answers in a+ biform. a) i b) 7i c) 6 + i d) + i i. Find each power of i. i ( i) 6 7 a) i b) i c) i d) i e) f) Teaching Notes: Most students find objectives and fairl straightforward. Encourage students to keep their work neat and organized to avoid errors with objectives and. Some students have more success with problems c) and d) if the multipl the comple conjugates off to the side and then put the final result within the problem as the solve it. Refer students to the Sum or Difference of Comple Numbers, and Comple Conjugates charts. Answers: a) i, b) i, c) -, d) 0i, e), f) i, g) 6i, h) 6 i ; a) -i, b) 6+i, c) --i; a) -8, b), c) 8+8i, d) -+9i, e) 6, f) -i; a) -i, b) 7 i 8, c) i, d) 6 7 + i ; a) i, b), c) i, d) -, e) i, f) -i M- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form I Name Date Find each root. Assume that all variables represent nonnegative numbers.. 8 6.. 8.. 6 6 8.. 6... Simplif. Assume that the variables represent an real numbers. 6. 6 6. 7. 9 7. If f() =, find the function value. 8. f(6) 9. f(9) 8. 9. (a) Identif the domain and then (b) graph the function. 0. f() = 0. - - - - - - - - - - E- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form II Name Date Find each root. Assume that all variables represent nonnegative numbers... 00 6.. 8. 6. 6 8.... Simplif. Assume that the variables represent an real numbers. 6. 7. 6 7 6. 7. If f() = 8. f() 9. f(), find the function value. 8. 9. (a) Identif the domain and then (b) graph the function. 0. f() = 0. - - - - - - - - - - E- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form III Name Date Find each root. Assume that all variables represent nonnegative numbers.. 8 0 6.. 7.. a b... 7 7 0 z.. Simplif. Assume that the variables represent an real numbers. 6. 6 9 6. 7. 7 7. If f() =, find the function value. 8. f() 9. f() 8. 9. (a) Identif the domain and then (b) graph the function. 0. f() = 0. - - - - - - - - - - E-6 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form I Name Date Use radical notation to write each epression. Simplif if possible. Assume that all variables represent positive numbers... 6 7... 9... Write with positive eponents. Simplif if possible. Assume that all variables represent positive numbers.. 6. 7.. 6. 7. Use the properties of eponents to simplif each epression. Write with positive eponents. Assume that all variables represent positive numbers. 8. 9. 6 7 8. 9. Use rational eponents to simplif each radical. Assume that all variables represent positive numbers. 0. 6. 8 6 0.. Use rational epressions to write as a single radical epression. Assume that all variables represent positive numbers... 6 E-7 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall..

Additional Eercises 7. Form II Name Date Use radical notation to write each epression. Simplif if possible. Assume that all variables represent positive numbers.... 8 6 0 (9 ).... ( m ). Write with positive eponents. Simplif if possible. Assume that all variables represent positive numbers.. 6. 9. 6. 7. 7. Use the properties of eponents to simplif each epression. Write with positive eponents. Assume that all variables represent positive numbers. 8. 9 0 0 9. 8 8. 9. Use rational eponents to simplif each radical. Assume that all variables represent positive numbers. 0. 6 0.. ( 7). Use rational epressions to write as a single radical epression. Assume that all variables represent positive numbers.. a b.. ( )( ) E-8 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall.

Additional Eercises 7. Form III Name Date Use radical notation to write each epression. Simplif if possible. Assume that all variables represent positive numbers... ( 8) (6 )... (6 ).. 6 (6 ). Write with positive eponents. Simplif if possible. Assume that all variables represent positive numbers.. ( ). 6. 6 a 9 6. 7. 7 7. Use the properties of eponents to simplif each epression. Write with positive eponents. Assume that all variables represent positive numbers. 8. 9. ( ) 6 ( ) 8 8. 9. Use rational eponents to simplif each radical. Assume that all variables represent positive numbers. 0. 9 ( ) 0.. 9 ab. Use rational epressions to write as a single radical epression. Assume that all variables represent positive numbers.. 6.. Factor from 8. E-9 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall.

Additional Eercises 7. Form I Name Date Simplif.... 8... 7 7. 6... 6. 7 0 6 6. 7. 8a 7. 8. 0 8. 9. 9. 0. 08 6 0.. 6 6a.. 8.. 9 6 6. z 6z 9z.. E-60 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form II Name Date Simplif.. 0 7.. 7ab.. 6 7... 8. 8. 6. 9 6 6. 7. 8. 9. ab 8 7 7. 8. 9. 0. 6 0 6 0.. a b a b 7... a a 7 6... 9. E-6 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form III Name Date Simplif.. 6 7.. a b.... 6. m n 6 7 8 8... 6. 7. 6 7. 8. 8. 9. 9 6 z 9. 0.. 6 80 9 6 0... z z 6 6 6 9 7... 96a b ab 8 6 9 7 9.. E-6 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form I Name Date Add or subtract.. 6. 8. 7. 6..... 6. 0 0 9 8. 6. 7. 7 6 6 9 7. Multipl, and then simplif if possible. 8. 9. 0. 8 9. 7 7. 7.. 6 8. 9. 0..... E-6 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form II Name Date Add or subtract.. 8 0. 7 7..... 6. 7. 9 6 8 6 6 8... 6. 7. Multipl, and then simplif if possible. 8. 6 9. 9 9 7 7 0. 8. 0. 6. 6 8. 8. 9. 0..... E-6 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form III Name Date Add or subtract.. 0..... 6. 6 7 8 88 6 88 8 8 8 6 7.... 6. 7. 76 6 7. Multipl, and then simplif if possible. 8. 9 9. 0. 7 7. 9.. 6 8. 9. 0..... 8 8. E-6 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form I Name Date Rationalize each denominator...... 8.. 7.. 8. 6. 6. Rationalize each numerator. 7. 7. 8. 0 8. 9. 9. 8 0. 0.... 6. E-66 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form II Name Date Rationalize each denominator... 7..... 9... 6. a a b 6. Rationalize each numerator. 7. 7. 8. 7 8 8. 9. 0. 7 6 9. 0..... E-67 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7. Form III Name Date Rationalize each denominator... 0 6.... 8 9 6... 6 6. 6. 6. Rationalize each numerator. 7. 8. 0 6 7 7. 8. 9. 7 9. 0. 6 z 0.. 7.. 6. E-68 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7.6 Form I Name Date Solve.. 6.... 6 0. 7. 7 7 6. 8... 6. 7. 9 7. 8. 9. 8. 9. 0.. z z. z z. Find the length of the unknown side in the triangle. 0.... 7 in. in.. The formula v gh gives the velocit v, in feet per second, of an object when it falls h feet accelerated b gravit g, in feet per second squared. If g is approimatel feet per second squared, find how far an object has fallen if its velocit is 0 feet per second.. E-69 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7.6 Form II Name Date Solve.. 6. 0.. 6...... 6. 8 8 7. 7 6 6. 7. 8. 7 7 8. 9. a a 8 0.. 8. 9. Find the length of the unknown side in the triangle. 9. 0.... 8 m m. The formula for the period of a pendulum, P, in seconds, is l P, where l is the length of the pendulum in feet. What is the length of a pendulum whose period is seconds?. E-70 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7.6 Form III Name Date Solve.. 0. 6 7. 9 8 0. 8 9..... 6. 6. 8 7 7. b b 8. z 8z 0 9. 0. 7.. 7. To the nearest tenth of a meter, find the length of the unknown side in the triangle. 6. 7. 8. 9. 0.... 9 m m. A wire is needed to support a telephone pole that is feet high. The cable will be anchored to a stake that is 7. feet from the base of the pole. To the nearest tenth of a foot, how much cable is needed?. E-7 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7.7 Form I Name Date Write in terms of i.. 8..... Perform the indicated operation. Write answers in the form a + bi.. 6. 6. 00 7. ( i) + ( + i) 8. (6 i) + ( + 7i) 9. i 6 i 0. i( i). (7 + i)(7 i). ( + i). i i.. 6. 7. 8. 9. 0.... Simplif. Find each power of i.. i. i.. E-7 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7.7 Form II Name Date Write in terms of i.. 7.. 9 6.. 0 8. Perform the indicated operation. Write answers in the form a + bi.. 8. 0 6. 00 0 7. (7 + i) ( i) 8. (8 + i) ( 6i) 9. i 7 i.. 6. 7. 8. 9. 0. 7i( i). (6 i)( + i). ( + 7i) 0.... 6 i. Simplif. Find each power of i.. i 7. i 7.. E-7 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Eercises 7.7 Form III Name Date Write in terms of i.. 6.. 9... Perform the indicated operation. Write answers in the form a + bi.. i.. 9 78 6. 7. (9 + i) ( 7 i) 8. i i 8 9. i 7 8i 0. (i)( i). ( + i)( i). (6 9i). 6. 7. 8. 9. 0.... 7i i. Simplif. Find each power of i.. i. i i.. E-7 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Section 7. Radicals and Radical Functions Objective: Find values and roots with different indices.. Suggested Format: Think and Pair Time: 0 minutes Simplif each root. Assume that variables represent positive real numbers.. 0... 9. 6 6.. 6( ) 8... Use f ( ) = + for question 6 8. 6. Find f ( 0). 6. 7. Find f ( ). 7. 8. Find f ( ). 8. 9. Find the length indicated b. Round our 0. answer to the nearest hundredth. 0 A- 7 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Section 7.6 Rational Equations and Problem Solving Objective: Appl knowledge of solving equations with radicals to real life eamples.. Suggested Format: Small Group Time: minutes An accident investigator is often responsible for determining the speed at which a vehicle was traveling before colliding with another object. Investigators use the formula: S =. cd where S is the speed of the vehicle (in miles per hour), c is the coefficient of friction between the surface of the road and the tires of the vehicle, and d stands for the length of the longest skid mark on the surface (in feet). If the road is dr the value of c normall ranges between 0.69 and 0.7 for most cars.. Find the speed of a car that left a -foot long skid mark before hitting a tree. Let c = 0.7. Speed. A defendant in a vehicular homicide trial is arguing that he was not traveling over 0 mph when he struck another vehicle. What is the maimum length of the skid mark could leave if this was so? (Assume roads were dr and c = 0.7.) Length of skid mark A- 8 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form A Raise to the power or take the root. Assume that all variables represent positive numbers. Write our answers using onl positive eponents.. 0.. 0 0.. 6.. 96 z.. a a + a. 6. 6a b c 6. Simplif. Use absolute value bars when necessar. 7. 6a b 7. Rationalize the denominator. Assume that all variables represent positive numbers. 8. 0 8. 9. 0. ab a b + 9. 0. Use a calculator to approimate the number to three decimal places.. 0. T- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form A cont d Perform the indicated operations. Assume that all variables represent positive numbers.. 8 z + z.. 8.. ( 0 0 ).. ( ). 6. ( )( ) + 6. Perform the indicated operation and simplif. Write the result in the form a + bi. 7. 0 7. 8. ( i) ( 6 i) + 8. 9. ( i ) 9. 0. 6 i + i 0. Solve each equation.. 7 = +.. + =.. =.. Find the distance between the two points. (, ) and (, 8). Find the midpoint between the two points.. (, 6) and (, 8) T- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form B Raise to the power or take the root. Assume that all variables represent positive numbers. Write our answers using onl positive eponents.. 9. 6. 8 7 9.. 6 9.... +. Simplif. Use absolute value bars when necessar. 6. 6. 7. ( ) 8 + 7. Perform the indicated operations. Assume that all variables represent positive numbers. 8. 8 a a a 8. 9. ( ) 9. 0. ( a )( a ) + 0.. ( )( + ). T- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form B cont d Rationalize the denominator. Assume that all variables represent positive numbers.. 7.. +. Rationalize the numerator. Assume that all variables represent positive numbers... Perform the indicated operation and simplif. Write the result in the form a + bi... + 6. 6. ( i ) ( 8 i) 7. i ( i) 8. ( i)( i) 7. + 8. 9. + i i 0. + i i 9. 0. Solve each equation.. + =.. + =.. + 6 = 0.. Find the distance between the two points. (, ) and (, ). Find the midpoint between the two points.. (, ) and (, 8) T- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form C Raise to the power or take the root. Assume that all variables represent positive numbers. Write our answers using onl positive eponents.. 6 7 a b c.. 8.. 8 7 6... Simplif. Use absolute value bars when necessar... 6. ( ) 6. Rationalize the denominator. Assume that all variables represent positive numbers. 6 7. 7. 8. 9. 6 + 6 8. 9. Use a calculator to approimate the number to three decimal places. 0. 0 0. Perform the indicated operations. Assume that all variables represent positive numbers.. 0. T- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form C cont d. 6 ( + 70 ).. ( ). +.. ( )( ) +.. ( )( ) Solve each equation. 6. 8 = 6. 7. + = + 7. 8. = 8. Perform the indicated operation and simplif. Write the result in the form a + bi. + + 9. 9. ( 0 i) ( 8i) 0. i ( i ) 0. +.. ( 6i)( i). i i. + i i... Find the distance between the two points. (, ) and (6, ). Find the midpoint between the two points.. (8, ) and (, ) T- 6 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form D Circle the correct answer. Raise to the power or take the root. Assume that all variables represent positive numbers.. 8 i 7 b. 7 c. i 7 d. not a real number. 6 6a b 6b a b. 6ab a c. ab a d. 6ab a. 6a b 9 8 a b b. a b b c. 8a b d. not a real number. a b 0 a b b. a b c. a b d. a b. + 7 + b. 9 c. 6 + d. + Simplif. 6. ( ) 8 9( ) b. c. ( ) d. 9 T- 7 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form D cont d Perform the indicated operations. Assume that all variables represent positive numbers. 7. 98 8 b. c. d. 8. 9 + 7 67 b. c. 8 + d. 9 9. ( ) 8 + 6 b. 8 + 6 c. + 6 d. + 6 0. ( + 7)( ) 6 + 7 7 b. + 7 7 c. 6 + + 7 7 d. 7 7. ( + )( ) b. c. 6 d. 9 Use a calculator to approimate each to decimal places.. 7.799 b..7 c..8 d..76. 0 0.9 b. 0.00 c. 0.9 d. 0.97 T- 8 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form D cont d Rationalize the denominator. Assume that all variables represent positive numbers.. b. c. d. 0. + + b. + 7 c. + 7 + d. + 7 + 6. b. c. d. Solve. 7. + 6 + 6 = b. 0 c. 0 d. Ø 8. + 8 = 7 8 b. 0 c. 6 d. Ø 9. = + b., 6 c., 6 d. 0, Perform the indicated operation and simplif. Write the result in the form a + bi. 0. ( i) ( 6 i) i b. 8i c. 0 8i d. 9 T- 9 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form D cont d. ( i)( + i) 9 + i b. 6 + 7i c. + 7i d. + i. 6 i i b. c. i d. + i. + i + i b. 7 i c. 7 i d. 7 + i. Find the distance between the two points (, ) and (, 6). b. c. d.. Find the midpoint between the two points ( 7, ) and ( 8, ) 9, b., c., d. ( 7, ) T- 0 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form E Circle the correct answer. Raise to the power or take the root. Assume that all variables represent positive numbers.. 6 8 b. 6 8 c. 6 8 d.. 8 6 z z b. 6 z c. z d. z. ( 9) 7 b. 7 c. 9 d. 9. 8 b. 7 0 c. 0 d.. z z b. z c. z d. z 6. 6 b. c. d. 6 T- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form E cont d 7. Simplif. ( ) b. c. d. Use a calculator to approimate to decimal places. 8.. b..7 c..6 d..9 Rationalize the denominator. Assume that all variables represent positive numbers. 9. 6 b. c. d. 0. + + + b. c. + d.. 9 b. c. d. Perform the indicated operations. Assume that all variables represent positive numbers.. 7 7 b. c. d.. ( 0 ) b. 0 c. 0 d. 0 T- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form E cont d. ( 7 )( 7 + ) Solve. 9 b. 9 8 + c. 9 + 8 + d. 0 +. = + 0 b. 8 c. d. Ø 6. 6 6 = 9 b. c. 7 d. Ø 7. + =, 6 b. 6 c. d. Ø Perform the indicated operation and simplif. Write the result in the form a + bi. 8. 6 i b. i c. d. i 9. ( + i) ( i) 9 + i b. + i c. 9 + 7i d. 6 9i 0. ( i ) 9 + 0i b. 0i c. 0i d. 9 0i T- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form E cont d. ( 8 i)( 7 + i) 8 i b. i c. 6 i d. 6 0i. 6 i i 0 b. + 6i c. i d. i. i + 6i 7 9 0 0 i b. c. 6 i i d. 6 0 + i. Find the distance between the two points (, ) and (7, 8). b. c. d. 69. Find the midpoint between the two points (, 7) and (, 9) (, 6) b. (, ) c. (, 8) d. (, ) T- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form F Circle the correct answer. Raise to the power or take the root. Assume that all variables represent positive numbers.. 8 6 6 b. 9 6 8 c. 6 6 d. 6 6 6. 0 b. c. 0 d.. 9 6 b. 6 c. 6 d. 6. 7 7 9 b. c. 8 d.. ( ) 8 6 9 6 8 b. 9 6 c. 6 9 d. 8 6 Simplif. 6. ( ) b. ( ) c. ( ) d. T- Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form F cont d Rationalize the denominator. Assume that all variables represent positive numbers. 7. 7 9 7 7 b. 7 c. 7 9 d. 7 9 8 8. b. 0 c. d. 0 9. 6 6 + b. + c. d. Use a calculator to approimate to decimal places. 0. 7.9 b..8 c..67 d..6 Perform the indicated operations. Assume that all variables represent positive numbers.. 80 + 0 6 b. c. 9 7 d.. ( ) 6 + 9 b. 9 c. 9 d. 6 + 9 T- 6 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form F cont d. ( 6 ) b. 6 c. d. 9 6. ( + 7)( 6) + 9 b. + c. d. + Solve.. + =, b., c., d. Ø 6. = 0 b. 7 c. d. Ø 7. = 7 0, b., c. 0, d. Ø Perform the indicated operation and simplif. Write the result in the form a + bi. 8. 8 6i b. i c. i d. 9. ( + i) ( 7 i) + ( 9 i) + 0i b. i c. 08 8i d. 0i 0. i( i ) i b. 8 6i c. 6 + 8i d. 6 + 8i T- 7 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Name: Instructor: Date: Section: Chapter 7 Test Form F cont d. i i i b. i c. + i d. + i. ( 7 i ) 9 + i b. 70i c. + 7i d. 7. 6 i + i i b. i c. i d. i. Find the distance between the two points (, 6) and (, 6). 6 b. 6 0 c. 7 d. 7. Find the midpoint between the two points (, 6) and (, 0) ( 8, 6) b. ( 9, 8) c. (, ) d. ( 8, ) T- 8 Copright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall