Graphing Square Roots - Class Work Graph the following equations by hand. State the domain and range of each using interval notation.
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1 Graphing Square Roots - Class Work Graph the following equations by hand. State the domain and range of each using interval notation. 1. y = x f(x) = x 1. y = x +. g(x) = 2 x 1. y = x h(x) = 2x 7. y = x y = x 8 1 Alg2 - Radicals ~1~ NJCTL.org
2 Graphing Square Roots - Homework Graph the following equations by hand. State the domain and range of each using interval notation. 9. y = x f(x) = 1 2 x 11. y = x 12. g(x) = 2 x y = 1 x + 1. h(x) = x y = 2x y = x Alg2 - Radicals ~2~ NJCTL.org
3 Working with Square Roots - Class Work Simplify each square root b 2 1. x 2. y 6. m 18. p x 6 6. c d8 8. m n2 0. y12 16 Alg2 - Radicals ~~ NJCTL.org
4 Working with Square Roots - Homework Simplify each square root a 6. x 8 6. m t x 9. h x d y g r8 6 Spiral Review 6. Factor: 66. Multiply: 67. Simplify: 68. Factor: 27m 1 (x 2y)(x 2 2xy + y) 2m n 7 m 7 n 2x2 x + Alg2 - Radicals ~~ NJCTL.org
5 Irrational Roots - Class Work Put in simplest radical form: c a x y m 8 n r 9 s p 2 q 10 r g h x 10 y a 7 y xy 2 0x 2 y a b 96a 9 b 91. 1m 2 n 6 120m n 6 Alg2 - Radicals ~~ NJCTL.org
6 Irrational Roots - Homework Put in simplest radical form: m 2 108m p x n r s p q 10 r x 20 y a b 1 c g 6 h j 1 k a b p q 80p 1 q m n 72m 7 n x y 1x 10 y 12 Spiral Review 11. Solve: 116. Factor: 117. Simplify: 118. Factor: -(x + 2) (x ) = 0 2x 2-16y 2 ( m n 2 )( m 6 n ) 12p 2 p Alg2 - Radicals ~6~ NJCTL.org
7 Adding and Subtracting Radicals - Class Work Simplify each expression x 27x x 12x 1. 8y + y 18y 1. 6m n 2 m mn kp + 6p 2 k 16. 2r 8r 12r Alg2 - Radicals ~7~ NJCTL.org
8 Adding and Subtracting Radicals - Homework Simplify each expression p p p 10. x x 6 x 11. 8m 6 n 8 + 2m 6 n a a y y 1. x 6 x + 12x Spiral Review 1. Simplify: 16. Factor: 17. Multiply: 18. Simplify: 12x 2 y 8x 6 y 8 6p + 12q (a + 7)(2a ) (-r s - t 2 )(-r 2 s - t) Alg2 - Radicals ~8~ NJCTL.org
9 Multiplying Radicals - Class Work Multiply the following. Make sure answers are in simplest radical form. 19. ( 2)(2 ) 160. ( )( 2) 161. ( 2 6)( 12) (x 2 11) 16. ( 1x)( 2 2x) (2 + ) 16. 6( 6 + 7) ( 6 7) 167. ( + )( 2 ) 168. ( 6 )( 6 6) 169. ( + )( 6) 170. (2 )(1 + 2) 171. (2 + 6) (7 10) ( )( 2 + ) Multiplying Radicals Homework Multiply the following. Make sure answers are in simplest radical form. 17. ( 6)(7 ) 17. (7y )(2 ) 176. ( )( 12) 177. ( 12) x( x) 179. (2 ) 180. ( 2 6) 181. x(2 1x ) 182. ( 2)(2 ) 18. ( + 2 )( 6) 18. (2 2 )(2 6) 18. (1 + 7) ( + 2)(1 ) 187. (8 6) (1 2 )(1 + 2 ) Spiral Review 189. Factor: 190. Factor: 191. Simplify: 192. Simplify: 9m 2 + 0m x y 1 (a b - )(a b - ) 12a b 2ab Alg2 - Radicals ~9~ NJCTL.org
10 Rationalizing the Denominator - Class Work Simplify: Alg2 - Radicals ~10~ NJCTL.org
11 Rationalizing the Denominator - Homework Simplify: Spiral Review 217. Simplify: 218. Multiply: 219. Factor: 220. Simplify: a b 6 (2x )(x + 8) x 2 11x ( a b 2 ) Alg2 - Radicals ~11~ NJCTL.org
12 Cube Roots - Class Work Simplify: x a b x c1 d x y 7 z r 6 s 9 t mn 2 m 2 n p ab 6a b 7 c 1 Cube Roots - Homework Simplify: x a 6 b p j27 k j k m x 6 y 7 z 8 2. ab 6a b c 2. 6x 2 z 0x y z Spiral Review 2. Simplify: 26. Multiply: 27. Multiply: 28. Solve: x (x ) (2a b)(a 2 + 2ab + b 2 ) (x 2y)(x + 2y) 2(p ) (p + 1) = 1 Alg2 - Radicals ~12~ NJCTL.org
13 n th roots - Class Work Simplify: x x x 10 y 1 z x e29 f m n x 6 y z x y z x 16x 6 y 1 z m n 2 p (p ) 262. (2x 1) (r + p) x 8 y x 267. x m2 2r 2 n x2 y t 271. p t 272. x Alg2 - Radicals ~1~ NJCTL.org
14 n th roots - Homework Simplify: x x x 1 y z x p2 q a 1 b x 9 y 10 z x y z 81x 2 y z ab 6 6a 1 b (m + 2) 28. (2r ) (2y 1) n 8 p y x m m 2n 291. x t r y x 29. 8x 9 6 r Spiral Review 296. Factor: 297. Multiply: 298. Simplify: 299. Simplify: 1p 2 1 7( 10 2) ( a b 2 ) ( 12m n ) 2 Alg2 - Radicals ~1~ NJCTL.org
15 Rational Exponents - Class Work Simplify: 00. ( 2) () (12) 0. (27) 0. ( 1 8 ) 1 0. (16) 7 Write each expression without the radical m rs 2 t x 9 Write each expression using a single radical. 09. x a 1 b 2 c 11. e 1 2f 1 g Simplify. Leave answers with positive exponents. 12. (x 6 ) (27y 6 ) 1. (2a 1 2 ) (16b 2 ) (c 2 10 ) 17. x x 18. y y z1 z 1 2z (2m ) 2 Alg2 - Radicals ~1~ NJCTL.org
16 Rational Exponents Homework Simplify: 21. ( 12) () 2 2. (16) 2. ( 27) 1 2. ( 1 2 ) () 2 Write each expression without the radical p 28. r s t x 6 Write each expression using a single radical. 0. x 1 1. a 1 6b 2 c 2. m 1 n 2p Simplify. Leave answers with positive exponents.. (x ) 1 2. (y ) 2. a 1 6. (9b 2 7) 1 7. (c 8) 9 8. x x 1 9. y y m6 m 1 1 m 1. (16x 12 ) Spiral Review 2. Simplify:. Multiply:. Simplify:. Factor: a b a 2 b 2 (x + y)(x y) (2a 2 b ) 1 8y Alg2 - Radicals ~16~ NJCTL.org
17 Solving Radical Equations - Class Work Solve each of the following equations. 6. 2x = 2 7. a + 1 = 8. 2x = = 2 2t 0. (2p ) 1 = 2 1. m + 2 = 2m 2. x + 1 6x 9 = 0. (8) 1 2 = (m) 1 2. t + 1 = t 1. 2x + = 2x + 2 Alg2 - Radicals ~17~ NJCTL.org
18 Solving Radical Equations - Homework Solve each of the following equations. 6. g = x 1 = 8. 2m = = 2 6 b 60. (x 2) 1 = y + = 2y x + 2 8x 7 = 0 6. (6) 1 = (m) 1 6. t + t = 2 6. x + = x + 1 Spiral Review 66. Simplify: 67. Multiply: 68. Multiply: 69. Simplify: a (2x y)(x y) 2( ) ( m 2 n ) b c d + 1 Alg2 - Radicals ~18~ NJCTL.org
19 Complex Numbers - Class Work Simplify using i. 70. i i i 71. 2i i 6i 8i 72. i i i 7. i i 7i i 7. 2i 2i 2i 7. 6i i i i 76. i i i i i 81. i x 9 1x p 10p b 89. 8a x 6 y m n 92. 8a 2 b x 8 y 12 Alg2 - Radicals ~19~ NJCTL.org
20 Complex Numbers - Homework Simplify using i. 9. i i i 9. i 2i 9i i 96. i i 2i 97. i i i i 98. 2i i 7i 99. i i i 7i 00. i i i i 2 0. i 1 0. i i i m m x 6 12x b a x y r x m 7 n 20. 2a 6 b 1 Spiral Review 21. Multiply: 22. Multiply: 2. Factor: 2. Simplify: (p + q)(9p 2 pq + q 2 ) x y(x y 1) 6x + 27y x y x 2 y 2 Alg2 - Radicals ~20~ NJCTL.org
21 Adding, Subtracting, and Multiplying Complex Numbers - Class Work Simplify: 2. (6 + i) ( + i) 26. ( + 2i) + ( 2 i) 27. ( i) ( i) 28. ( + i) + ( i) 29. (7 + i) ( 2 2i) 0. ( 2i) ( i) 1. ( 2i) 2. 2i( 6 + i). i( i). 6( + i). (6 + i)( + i) 6. (7 + i)( 2 2i) 7. ( 2 + 9i)(1 i) 8. ( i)( + i) 9. ( 2i)( i) 0. (8 i)(1 i) 1. ( 2i) 2 2. ( 6 + i) 2 Alg2 - Radicals ~21~ NJCTL.org
22 Adding, Subtracting, and Multiplying Complex Numbers - Homework Simplify:. ( 1 + i) + ( 2 i). (7 2i) ( i). (2 + i) + (8 + 2i) 6. ( + 9i) + ( 9i) 7. (10 7i) ( i) 8. (2 + i) (8 + 2i) 9. ( 2 i) ( + i) 0. (7 + 2i) + ( + 2i) 1. 6( 6i) 2. 2i( i). i( + 2i). i(1 i). (2 + i)(8 + 2i) 6. ( + 9i)( 9i) 7. (10 7i)( i) 8. ( 6 i)(2 7i) 9. (6 i) ( 7 + 2i) 2 Spiral Review 61. Multiply: 62. Multiply: 6. Work out: 6. Simplify: (q )(q 2 q 8) -2x 2 (y + z) (x ) x c+1 y d Alg2 - Radicals ~22~ NJCTL.org
23 Dividing Complex Numbers - Class Work Simplify 6. 2 i 66. i i i i 69. i i i 72. i 2i i 7. i 1 i 1 +i 7. + i i 2 9i 77. 2i 1 i i i + i 80. i 2i i + i i 8. i + 2i 8. 9 i 2i Alg2 - Radicals ~2~ NJCTL.org
24 Dividing Complex Numbers - Homework Simplify 8. i i 87. 7i 88. i i 89. i 90. i 91. 7i i 2i i 9. 2i i 9. 2 i 2 + i 96. i i 97. 2i i 6 + i i + 2i i 1 i 01. 2i i i i i 2 + i 0. 2i 1 + i Spiral Review 0. Factor: 06. Multiply: 07. Multiply: 08. Simplify: 6m 2 19m 7 (xy 1)(xy + 1) (2x y)(x 2 + 2xy + y 2 ) c d a b + 1 Alg2 - Radicals ~2~ NJCTL.org
25 Radicals Answer Key Alg2 - Radicals ~2~ NJCTL.org
26 Alg2 - Radicals ~26~ NJCTL.org
27 Not a real number Not a real number Not a real number 0. b x 2 2. y. m 9. p Alg2 - Radicals ~27~ NJCTL.org
28 . 12 x 6. c d 7 m 9 9. n y a. x 6. m 6 7. t 6 8. x 2 9. h x d y g1 6. r 6 6. (m 1)(9m 2 + m + 1) 66. x 8x 2 y + xy + xy 2 2y n2 m 68. (x + )(2x ) c 2 7. Not a real number a x 2 y x 8. 6m n r s r 8. 2 pq r g h 7 6g x y 88. 1a y 0a x 1 y a 7 b 2 6ab 91. 0m n m m p p x n rs p 2 q r 2 2r x 10 y 108. a 2 b 7 c ab Alg2 - Radicals ~28~ NJCTL.org
29 g h j 1 k 2 jk ab 7 ab 112. p 9 q 17 pq 11. m 7 n 7 2m 11. 8x x y x = (x y)(x + y) m 9 n 118. p(p 1) x 1. 22y 2 2y 1. m n m 1. p 2 k 16. r 2 2r 6r 2 r p p x 2 x m n a 6 a 1. 10y y 8y y 1. 8 x y 1. x (p + q)(16p 2 20pq + 2p 2 ) 17. 6a 2 a r t s x x y x x x + 1x Alg2 - Radicals ~29~ NJCTL.org
30 (m + ) (xy 1)(9x 2 y 2 + xy + 1) a7 b a a b x 2 + x (x 1)(x + ) b6 a x ab x c d xy 2 xyz r 2 s t 21. 1mn p 2 6m 2 n a 2 b c a 2 bc x 26. 9a 2 b p j k jk jm 22. x 2 y 2 z 2 yz a 2 b 2 c 7ac x yz yz a b x 2 62y p = Not a real number x x 2. x 2 y z 2. x Alg2 - Radicals ~0~ NJCTL.org
31 2. e e f n 2 6 m n 27. x 27x 2 y z x yz 2 y 29. 8x 2 y z x 2 yz n p 7 m n 261. p 262. (2x 1) (r + p) 26. 2x 2 y x r m2 n 6 n 269. x2 y y t p x 2x 27. Not a real number x 276. x 277. x yz x p p q ab 8 a 7 b x 2 y 2 z 2 7xy 2 z x y z 6 x 2 z a b 8 6 a b Cannot be simplified 28. (2r ) 286. (2y 1) np 2 7 n 288. x2 y x 289. m2 m mn6 2n x x r t 29. r 16y 2y 29. 2x r r 296. (12p 1)(12p + 1) a 9 b -6 n m m r 1 s 2 t 08. x x ab 2 c e 6 f g x 1. 2y a1 2 a 2 1. b c 17. x y z 1 12 z m 6 Alg2 - Radicals ~1~ NJCTL.org
32 p r st x 2 0. x 6 1. ab c m n 0 p 1. x 2. y 2 2. a a b 7. c 6 c 8. x 9. y 7 0. m m 1 8x 9 2. b a. 9x 2 y 2. 16a8 b 16. (1 2y)(1 + 2y + y 2 ) 6. x = 2 7. a = x = 8 9. t = p = 2 1. m = 2 2. x =. m = 2. No solution. x = 0 6. g = 8 7. x = 6 8. m = b = x = No real solution 62. x = 6. m = 2 6. t = 6. x = 1 a(d + 1) 66. bc 67. 8x 2 10xy + y m 8 n i i i i i 79. i 80. i i 8. 2x p 87. i 88. 6ib ai x y i 2y 91. 6m 2 ni 2n 92. a b i 9. x y 6 i 9. 9i Alg2 - Radicals ~2~ NJCTL.org
33 i i i i i 07. i i 11. m 12. 1x i 1. 11b i 1. a i x 2 y i x 17. r 6 i 18. 2xi x 19. m ni 6mn 20. a b 7 i p + q x 7 y 2 - x y 2. (x + y)(16x 2 12xy + 9y 2 ) 2. y x i i i i i i i. - 12i. 2 18i i i i i 0. 11i i 2. 12i i i i i i i i i i. -1 i i i i i i i 61. q 1q 2 2q x 2 y 2x 2 z 6. x 9x x 27 xd 6. y(c + 1) 6. -2i 66. i 67. 2i i 69. i 70. i i i i Alg2 - Radicals ~~ NJCTL.org
34 i i i i i 1 i i 1 7 i i i i i 86. 2i 87. i i 89. -i 90. i 91. i i i 2 + 8i i i i i i i i i i i (m + 1)(2m 7) 06. 9x 2 y x y 08. c(b+1) ad Alg2 - Radicals ~~ NJCTL.org
Graphing Square Roots - Class Work Graph the following equations by hand. State the domain and range of each using interval notation.
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