Name: Date: Section.1 Etra Practice BLM 1. Epress each radical as a simplified mied radical. 0 98, 0 6 y, 0, y 0. Epress each mied radical as an equivalent entire radical. 1 9, 0 y 7 y, 0, y 0. Order each set of numbers from least to greatest., 0, 1, 18,, 6, 6. Simplify each epression. Identify any restrictions on the values of the variables. + + 9 9 + 9 16y + y 7. Simplify each epression. 6 8 y 6 + 7 6 8. What is the perimeter of the right triangle shown? State the answer as an eact value. 60,, 16,, 1, 6, 0. Simplify each epression. 7 11 11+ 8 11 + 9 6+ 1 6+ 6 7y + 7y. Simplify each epression. 0d + d 10e 90e + 0e + 1 8 + 7 6 + 7 8 7 Copyright 011, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-0788-6
Name: Date: Section. Etra Practice BLM 1. Multiply. Epress each answer as a mied radical in simplest form. ( 6 )( ) 1 ( 10 ) ( ) 1 8 1 ( 7 )( 7 ). Simplify each epression. For part, identify the values of the variable that make the radical epression a real number. 10 ( 10 + ) 1 ( ) ( 1+ ) ( ). Multiply using the distributive property. Simplify each epression. ( 1+ )( + ) ( + 7)( 7 + ) ( 1+ )( 1 ) ( + ). Multiply and simplify each epression. State any restrictions on the values for the variables. ( + 1)( ) ( )( + ) ( 1)( + ) ( ) + 1. Divide. Epress each answer in simplest form. 0 7, > 0 90 1 18 6, > 0 6. Rationalize each denominator. Epress each radical in simplest form. 10 7 8 1 1 7 70 7. Rationalize each denominator. Simplify. 1 6 + 6 6 18 8, > 0 + 8, > 0 8. Rationalize each denominator. Simplify. + 1 1 6 6 Copyright 011, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-0788-6
. Name: Date: Section. Etra Practice BLM 6 State the restrictions on the values for each variable. 1. Solve for in each equation. + = 7 = = 0 =. Solve and verify. 7 + 1= 1 y + 1 y = 1 8 1+ v = = + 1. Solve and verify. m = m 1= + 1 n n = + = + 1. Solve and check. w+ 1= w + + = y+ 1 = + 10 = 6. Solve each radical equation. + = = 8 y 7. John solves the equation + 6 =. He determines two solutions: = and =. Identify whether either of these values is etraneous. d 8. The equation t = describes the time, t,.9 in seconds, for an object to fall from a height of d metres. Determine the original height of an object that takes. s to reach the ground. Epress the answer to the nearest tenth of a metre.. Solve each radical equation. + = y 1= y + 1 + = p = p Copyright 011, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-0788-6
Name: Date: Chapter Test Multiple Choice For #1 to, select the best answer. 1. Which mied radical is equal to in simplest form? A a b B 9a 6b C ab 86 D ab. Which epression represents written as an entire radical? A ab B C 1ab D a b 1a b 86a b ab. What is the sum of 0 18 + 8? A B 10 C 1 0 D 10. Which epression represents ( + ) when it is epanded and written in simplest form? A 7 B 9 C 7 + 10 D 7. Fran and Jaspreet rationalize the denominator of a radical epression. They record their partial solutions. Fran Jaspreet 18 Step 1 6 Step 1 = 18 Step = ( 6 6) Step = 6 Step = Step Which student made an error, and in which step? A Fran made an error in step. B Jaspreet made an error in step. C Fran made an error in step. D Jaspreet made an error in step. Short Answer 6. Arrange the numbers 9,,, 19, and 6 in order from least to greatest. BLM 7 7. Determine algebraically whether the statement 16 + 9 = is true or false. 8. The area of a rectangle is square units and its width is 6 units. What is the eact length of the rectangle in simplest form? 9. What is the epression ( + 1 ) in simplest form? 10. Solve r+ 1 = r+ 1 algebraically. State any restrictions on the values for the variable. 11. What is the quotient of + in simplest form? Etended Response 1. The velocity, v, in metres per second, of a roller coaster at the bottom of a hill is related to the vertical drop, h, in metres, and the velocity, ν 0, in metres per second, of the roller coaster at the top of the hill by the formula v0 = v 0 h. Valerie simplifies the epression for the formula to v0 = v h. Is Valerie s simplification correct? Eplain your reasoning. Suppose the velocity at the top of a hill is 0 m/s and the velocity at the bottom of the hill is 0 m/s. What is the vertical drop of the hill? 1. Isolate the -variable in the radical equation, + + =. Verify by substitution whether the value determined for is a root of the equation. 1. Determine the roots of the equation y + 1 y = algebraically. Identify any restrictions on the values for the variable. Copyright 011, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-0788-6
Chapter BLM Answers BLM Chapter Prerequisite Skills 1. perfect square perfect cube perfect square both. 7 9 1. 1 1 6 1 1 1 1. y t g. 6 8. 0.0016 1 e) 16 777 16 f ) 0.1780 17 6. 1 1 1 1 9 m 6 d y 7. 17 6.8 1 = 1 = 8 0.189 8. ( 1 p ) st 9. 16.9 16.166 1.071.678 1 y BLM Chapter Warm-Up Section.1 1. 6, 6 81, 81 6, 6, 8, 8, 6 1, 1 e) 8, 8,,, 8. 11 16 ±1 11 e) 1 f ) 7.6 g) h) 0.. 7.9. 68.9.8 e) 0. f ) 0.9., 11, 1, 8, 9. 10 e) f ) 6. 0 8 0 18 e) 7. 7y + 9y am 6pm + y 6q y + qy Section. 1. 6s t 6 p 6b b + y e) n n f ) 10y + 8y. y a b t + 6. y y m 6mn t t. 18 p 8 0y. p ab 11y e) 10 + 6 f ) 6 + Section. 1. = 0. =, = ± 7. y 6t 6 m m e) 1 n n f ) y g) 6 + 9 h) + 9y + 1 y., p > 0, > 0 y y 1, y > 0 1, > 1. + 7 + y. 1 0 0 6 e) 6 f ) y + y y y BLM 8 BLM Section.1 Etra Practice 1. 6 1 7 11 y y. 80 6877 81 17y. 1,,, 0, 18,, 6, 60,, 16 1, 0, 6,. 1 11 16 + 8 6 10 7y. 1 d 6 10e 1 7 6., 0, 0, 0 7 y, 0 7. 7 y 8. 9 + 6 BLM Section. Etra Practice 1 1. 1 1 9 6. 0 + 1 + 6, 0. 6+ 16 + 7 9 9 + 1., 0 +, 0 + + 1, 0 Copyright 011, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-0788-6
. 6 6. 7. 0 0 + + 1 8. 0 0 1 8 + 10 1 0 19 BLM 6 Section. Etra Practice 1., = 6 0, = 16, = 0, = 88. = 8, 0 y = 0, y R v = 8, v 1 = 17, 1. m = 1, m = 1, ; = 1, 1 6. = 169, 0 = 8, 0, 7. The value = is etraneous. 6 8. 90.6 m BLM 7 Chapter Test 1. B. D. A. C. B 6. 6,, 19,,9 BLM 8 (continue 7. False. 16 + 9 = 7 8. 7 6 units 9. 1 10. r = 7, r 11. 6 1 1. No. Valerie s error is in taking the square root of each term of the radicand. The equation v 0 = v 0h cannot be further simplified. 60 m 1. = 1. y =, y = 7 is not a root of the equation. y n = 9 + 17. = 8,, n 0 = +, R y = 1, y = ; y = 1, y 1 no solution p =, p. w = 9, w 0 = 0, = 16; 0 y =, y 0 = 6, Copyright 011, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-0788-6