MAT 1033C -- Intermediate Algebra -- Lial Chapter 8 -- Roots and Radicals Practice for the Exam (Kincade)

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1 MAT 0C -- Intermediate Algebra -- Lial Chapter 8 -- Roots and Radicals Practice for the Exam (Kincade) Name Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. ) -24 Not a real number 8 ) C) 04, ) ) C) 26 Not a real number ) -2-2 C) ) 4) ) C) 8 62 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the function and give its domain and its range. ) f(x) = x + ) 0 y -0-0 x - -0

2 6) f(x) = x y 6) -0-0 x - -0 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the root. 7) x6 7) x -x C) x - x 8) x 2 x7 - x 7 C) - x7 x7 8) Find the decimal approximation for the radical. Round the answer to three decimal places. 9) C) ) Solve the problem. 0) A manufacturer's cost is given by C = 00 n + 700, where C is the cost and n is the number of parts produced. Find the cost when 64 parts are produced. $400 $2900 C) $7 $200 0) Simplify the expression involving rational exponents. ) 84/ 6 2 C) ) 2) 240/4 6,807 7 C) ) 2

3 ) 6/ C) 2 2 ) 4) (-8)2/ 4 Not a real number C) ) ) 2 6 -/2 ) 6 C) Not a real number 6) 6-/ ) C) Not a real number -024 Write with radicals. Assume that all variables represent positive real numbers. 7) (x4y4) / 4 4 x20y20 xy C) xy xy 4 7) Simplify the expression involving rational exponents. 8) / C) 26 8 Not a real number )

4 Write with radicals. Assume that all variables represent positive real numbers. 9) (8m4 + 2k2) -2/ 2 8m 4 + 2k2 2 8m 4 + 2k2 9) C) 2 8m 4 + 2k2 2 8m 4 + 2k2 Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. s-/2 20) (s-/7t/7) - 20) t-/6 s 69/4 t4/4 t 4/4 s69/4 C) t 29/4 s7/4 s 7/4 t29/4 2) x/ x6/ x- x4/ x22/ C) x4/ x22/ 2) Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form. 22) 4 x x2 x20/0 x7/9 C) x/20 x0/20 22) 2) x x0 2) x/2 x7/2 C) x4 x7/2 4

5 4 24) w w2 2w C) w/2 w2 24) Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. 2) (x /) 2 (x) 7/ 2) x9/ x9/ C) x2/ x2/ Multiply using the product rule. 26) 9x 4x 26) 6x x C) x2 6x2 27) 2xy 9xy 27) xy 8xy C) 22x2y2 4x2y2 Simplify the radical. Assume that all variables represent positive real numbers. 28) 9 x4 28) 9x4 x4 9 x2 C) 9 x4 9 x 29) 8x 4 x 29) x x x C) x 27 x

6 Multiply using the product rule. 0) 2 0) C) 4 Simplify the radical. Assume that all variables represent positive real numbers. ) 4 r 2 26 ) 4 r 4 r 4 C) 4 r r 2 4 Express the radical in simplified form. 2) C) 7 9 2) ) 62 ) 2 C) 6 6 4) 4 6 4) C) Express the radical in simplified form. Assume that all variables represent positive real numbers. ) - 2k7q8 2k7q8 k -2kq4 k C) -2kq4 2kq4 k ) 6) -64a8b 6) -4a2b a2b2 4ab ab C) 4 a2b2 4ab a2b2 6

7 7) y ) y7 y y 7 + y C) y7 - y y 7 y Simplify the radical. Assume that all variables represent positive real numbers. 8) 8 x20 8) x2 x x x C) x2 8 x4 x2 4 x2 Simplify by first writing the radicals with the same index. Then multiply. 9) 4 2 9) C) ) 4 40) C) Find the unknown length in the right triangle. Simplify the answer if necessary. 4) 4) 20 c 8 C) 2 7 7

8 b 7 42) 2 C) 42) Simplify the radical. Assume that all variables represent positive real numbers. 4) C) 6 4 4) Find the distance between the pair of points. 44) (, 6) and (-4, -) 0 2 C) 6 44) 4) (-, -2) and (, -6) 2 6 C) 2 8 4) Simplify. Assume that all variables represent positive real numbers. 46) C) ) 47) C) ) 48) 2x + 2 2x x 6 2x 7 2x C) 06x 0 06x 48) 8

9 49) 8 4 x7-4x 4 x 49) 4x 4 x7 8 4 x7-4x 4 x C) 4x 4 x 2 4 x 0) mp7 - m2p mp2 0) Cannot be simplified 8mp2 mp2 C) 2m2p mp2 2 ) ) C) 6 6 Multiply, then simplify the product. Assume that all variables represent positive real numbers. 2) (2 - ) C) ) ) ( + 7)( 2 - ) C) ) 4) (9 x + y)(9 x - y) 8x2 - y2 8x - y C) 8x + y 8x - 2 xy - y 4) Rationalize the denominator. Assume that all variables represent positive real numbers. ) ) -7-7 C)

10 6) - 24x y 6) - 7x y - 7x y2 x y C) - x 24xy y - 7x xy y 7) 2 7) 4 2 C) 2 2 Simplify. Assume that all variables represent positive real numbers. 8) 7 8) 2 89 C) 6 6 9) 7 9x2 9) 2x x 67x 8 C) 6x 9x 67x 2 9x Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. 4 60) 60) C)

11 6) ) C) Write the expression in lowest terms. Assume that all variables represent positive real numbers. 62) y + 7y y 62) + 7 y + 7 C) y 6) ) C) Solve the equation. 64) q - 4 = 4 {4} {6} C) ) 6) 7x = 0 {64} C) ) 66) 4 x = 9x C) )

12 Solve this equation. 67) p2-2p + 49 = p + {2} {8} C) {} {-} 67) 68) x = x {2, 9} {9} C) {9, 8} {2} 68) Solve the equation. 69) 4 + 6t - - 8t = C) ) 70) 2x + - x - 2 = {2, 8} {-2} C) {2} {, 8} 70) Write the number as a product of a real number and i. Simplify the radical expression. 7) -2 -i ± C) i -i 7) Solve the equation. 72) x + = + x - 4 {, 8} C) {-} {-,-8} 72) 2

13 Write the number as a product of a real number and i. Simplify the radical expression. 7) -8-9i i 9 C) ± 9 9i 7) 74) C) i 26 -i 26 74) 7) i 6-6i 6 C) ) Multiply or divide as indicated. 76) C) -2i 2i 76) 77) i 0 C) -i ) Add or subtract as indicated. Write your answer in the form a + bi. 78) (4 + 4i) - (-2 + i) 6 - i 6 + i C) 2 + i -6 - i 78) 79) ( + 2i) - (0 + 2i) + (8 + 4i) - + 8i - + 4i C) i -7-4i 79) Multiply. 80) (4-2i)(7 + 7i) -4i2 + 4i i C) i 42-4i 80)

14 8) i(7-4i)(8 - i) i 2i + i2 + 6i C) + 44i 68 - i 8) Write the expression in the form a + bi. 82) + i i i C) i i 82) 8) 4 + i + 2i 2-26 i 2-26 i C) i i 8) Find the power of i. 84) i6 - -i C) i 84) 8) i i - C) -i 8) 4

15 Answer Key Testname: MAT 0C CHAPTER 8 PRACTICE FOR THE EXAM WITH ANSWERS ) A 2) B ) A 4) C ) [-, ); [0, ) 0 y -0-0 x - 6) [0, ); [6, ) -0 0 y -0-0 x - 7) A 8) A 9) B 0) B ) A 2) B ) D 4) A ) A 6) A 7) B 8) C 9) C 20) C 2) D 22) C 2) D 24) C 2) B 26) D 27) C 28) B -0

16 Answer Key Testname: MAT 0C CHAPTER 8 PRACTICE FOR THE EXAM WITH ANSWERS 29) D 0) B ) D 2) A ) C 4) B ) B 6) A 7) D 8) A 9) B 40) C 4) C 42) D 4) D 44) A 4) A 46) A 47) A 48) B 49) C 0) C ) C 2) C ) C 4) B ) C 6) D 7) C 8) D 9) A 60) C 6) D 62) A 6) D 64) A 6) D 66) C 67) C 68) B 69) C 70) A 7) C 72) A 7) D 74) C 7) B 76) A 77) D 78) B 6

17 Answer Key Testname: MAT 0C CHAPTER 8 PRACTICE FOR THE EXAM WITH ANSWERS 79) B 80) C 8) C 82) A 8) C 84) D 8) A 7