Chapter 4: Radicals and Complex Numbers
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1 Section 4.1: A Review of the Properties of Exponents #1-42: Simplify the expression. 1) x 2 x 3 2) z 4 z 2 3) a 3 a 4) b 2 b 5) ) ) x 2 x 3 x 8) y 4 y 2 y 9) 10) 11) 12) 13) 14) 15) 16) 17) ( ) 18) ( ) 19) ( ) 20) ( ) 21) ( ) 22) ( ) 23) ( ) 24) ( ) 25) ( ) 26) ( ) 27) 28) 29) 30) 31) ( ) ( ) 32) ( ) ( ) 33) ( ) ( ) 34) ( ) ( ) 35) 36) 37) ( ) 38) ( ) 39) ( ) 40) ( ) 41) ( ) 42) ( ) 38
2 Section 4.2: A Review of the Properties of exponents (the power of 0 and negative exponents) #1-12: Simplify the expression. 1) x 0 2) y 0 3) 3 0 4) 2 0 5) ) ) (-2) 0 8) (-3) 0 9) 2c 0 10) 4b 0 11) (2x) 0 12) (3ab) 0 #13-38: Simplify the expression. Write the answer with positive exponents only. 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) ( ) 26) ( ) 27) ( ) 28) ( ) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39
3 Section 4.3: Definition of nth Root #1-30: Evaluate the roots.. 1) 2) 3) 4) 5) 6) 7 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) #31-42: Use a calculator to evaluate the expression, round to four decimal places. 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) Use a calculator to complete the table, round to two decimal places when needed. Use the table to help you state the domain of the function in interval notation. x Let ( ) h(x) 40
4 Section 4.3: Definition of nth Root 44) Use a calculator to complete the table, round to two decimal places when needed. Use the table to help you state the domain of the function in interval notation. x Let ( ) h(x) 45) Use a calculator to complete the table, round to two decimal places when needed. Use the table to help you state the domain of the function in interval notation. Let ( ) x h(x) 46) Use a calculator to complete the table, round to two decimal places when needed. Use the table to help you state the domain of the function in interval notation. Let ( ) x h(x) 41
5 Section 4.3: Definition of nth Root 47) Simplify a) b) ( ) c) 48) Simplify a) b) ( ) c) 49) Simplify a) b) ( ) c) 50) Simplify a) b) ( ) c) #51-58: Simplify the radical expressions. Use absolute values when necessary. 51) 52) 53) 54) 55) 56) 57) 58) #59-74: Simplify the expressions. Assume all variables are positive real numbers, so no absolute values will be needed in any of the answers. 59) 60) 61) 62) 63) 64) 65) 66) 67) 68) 69) 70) 71) 72) 73) 74) #75 79: find the domain of each 75a) ( ) b) ( ) 76a) ( ) b) ( ) 77a) ( ) b) ( ) 78a) ( ) b) ( ) 79a) ( ) b) ( ) 42
6 Section 4.4: Rational Exponents For this exercise set, assume that all variables represent positive real numbers unless stated. #1-6: Write the expression in radical notation, (do not simplify). 1) 2) 3) ( ) 4) ( ) 5) ( ) 6) ( ) #7-12: Write the expression using rational exponents rather than radical notation, (do not simplify) 7) 8) 9) 10) 11) 12) #13-30: Write the expression using positive exponents and radical notation, then simplify. 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) ( ) 28) ( ) 29) ( ) 30) ( ) #31-44: Simplify the expression using the properties of rational exponents. Write the final answer using positive exponents. 31) 32) 33) 34) 35) ( ) 36) ( ) 37) 38) 39) 40) 41) 42) 43) 44) #45-52: Use a calculator to approximate the expressions and round to 4 decimal places. 45) 46) 47) 48) 49) 50) 51) 52) 43
7 Section 4.5: Properties of Radicals For this exercise set, assume that all variables represent positive real numbers unless stated. #1-8: Use the multiplication property of radicals to multiply the expressions. Then simplify the result. 1) 2) 3) 4) 5) 6) 7) 8) #9-16: Use the division property of radicals to divide the expression. Then simplify the result. 9) 10) 11) 12) 13) 14) 15) 16) #17-52: Simplify the radicals. 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) 52) 44
8 Section 4.6: Addition and Subtraction of Radicals For this exercise set, assume that all variables represent positive real numbers unless otherwise stated. #1-28: Add or subtract the radical expressions if possible. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 45
9 Section 4.7: Multiplication of Radicals For this exercise set, assume that all variables represent positive real numbers unless otherwise stated. #1-26: Multiply the radical expressions. 1) 2) 3) 4) 5) 6) 7) ( )( ) 8) ( )( ) 9) ( )( ) 10) ( )( ) 11) ( ) 12) ( ) 13) ( ) 14) ( ) 15) ( )( ) 16) ( )( ) 17) ( )( ) 18) ( )( ) 19) ( )( ) 20) ( )( ) 21) ( )( ) 22) ( )( ) 23) ( )( ) 24) ( )( ) 25) ( )( ) 26) ( )( ) #27-36: Multiply the special products. 27) ( )( ) 28) ( )( ) 29) ( )( ) 30) ( )( ) 31) ( )( ) 32) ( )( ) 33) ( ) 34) ( ) 35) ( ) 36) ( ) 46
10 Section 4.8: Rationalization For this exercise set, assume that all variables represent positive real numbers unless otherwise stated. #1-22: Rationalize the denominator. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) #23-34: Rationalize the denominators by multiplying by the conjugate. 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 47
11 Section 4.9: Radical Equations #1-46: Solve the equation. Be sure to check your answers. If a solution is extraneous, say so in your solution. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) ( ) 22) ( ) 23) ( ) 24) ( ) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 48
12 Section 4.10: Complex Numbers #1-16: Simplify the expressions. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) #17-44: Perform the indicated operation, write your answer in standard form. 17) (6 + 2i) + (3 4i) 18) (4 3i) + (5 7i) 19) (3 6i) - ( 5 5i) 20) (8 + 9i) (7 9i) 21) (5 + 6i) + (3 5i) (3 + 2i) 22) (3-i) (4-i) (5 i) 23) (2i)(3i) 24) (-4i)(5i) 25) (-6i)(2i) 26) i(-5i) 27) 3i(2 5i) 28) 6i(5 + 4i) 29) -2i(4 + 9i) 30) 6i(2 i) 31) (3+2i)(5 i) 32) (4-3i)(5 + 2i) 33) (6-7i)(6+3i) 34) (5+i)(5 i) 35) (3+4i) 2 36) (6 i) 2 37) (1 i) 2 38) (2 3i) 2 39) (6+5i)(6 5i) 40) (4+3i)(4 3i) 41) (8+i)(8 i) 42) (7 2i)(7+2i) 43) (1+i)(1 i) 44) (3 i)(3+i) #45-56: Perform the division by multiplying by a factor equivalent to 1 that will take the i out of the denominator. 45) 46) 47) 48) 49) 50) 51) 52) 53) 54) 55) 56) 49
13 Chapter 4: Review 1) Simplify the expression. ) ) ) ( ) d) ( ) ( ) e) ( ) 2) Simplify the expression. a) x 0 b) ) Simplify the expression. Write your answer with only positive exponents. ) ) ( ) ) d) ( ) 4) Evaluate the roots ) ) ) 5) Write the domain in interval notation. ) ( ) ) ( ) 6) Simplify the radical expression. (Assume all variables represent positive real numbers.) ) ) ) 7) Simplify the expression. ) ) ) ( ) 8) Simplify the expression. Write your answer using only positive exponents. ) ) ) ( ) 9) Write the expression using radical notation. ( ) 10) Write the expression using rational exponents. 11) Multiply, then simplify. ) b) 12) Simplify. ) ) ) 13) Add or subtract. a) b) c) 14) Multiply, then simplify. a) b) c) ( )( ) d) ( ) e) ( )( ) 50
14 Chapter 4: Review #15-17: Rationalize the denominator. Simplify as much as possible. 15) 16) 17) #18-21: Simplify the expressions. 18) ) ) Subtract, write your answer in the form a+ bi (6-5i) (4-3i) 23) Multiply, write your answer in the form a+ bi (4-3i) 2 24) Divide, write your answer in the form a+ bi #25-29: Solve the radical equation if possible. 25) 26) 27) ( ) 28) 29) 51
15 52
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