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 quare Roots - lass Work Graph the following equations by hand. tate the domain and range of each using interval notation. 1. y = x f x = x 1. y = x + 4. g x = 2 x 1 5. y = x h x = 2x 4 7. y = x y = 4x 8 1 Alg2 - Radicals ~1~ NJTL.org
2 Graphing quare Roots - Homework Graph the following equations by hand. tate the domain and range of each using interval notation. 9. y = x f x = / 0 x 11. y = x g x = 2 x y = / 0 x h x = x y = 4 2x y = x 4 Alg2 - Radicals ~2~ NJTL.org
3 Working with quare Roots - lass Work implify each square root /7 /0/ / / b x 4 2. y 7. m /= 4. p /9 5. /44 6. A / G H D E F BE I BH /7 Alg2 - Radicals ~~ NJTL.org
4 Working with quare Roots - Homework implify each square root / =/ a x = 56. m /9 57. t /0 58. x P H / ? B@ =/ 6. Q H@ D BH I HH R E 87 piral Review 65. Factor: 66. Multiply: 67. implify: 68. Factor: 27m 1 (x 2y)(x 2 2xy + y) 0F G T F T G U 2x2 x + 5 Alg2 - Radicals ~4~ NJTL.org
5 Irrational Roots - lass Work Put in simplest radical form: c a x y m = n / r 5 s p 0 q /9 r g 8 h / x /9 y a \ y xy 0 40x 04 y /7 90. a 8 b 96a 5 b m 0 n 7 120m 4 n 7 Alg2 - Radicals ~5~ NJTL.org
6 Irrational Roots - Homework Put in simplest radical form: m 0 108m p x n / r 8 s = p 4 q /9 r x 09 y a b / c g 6 h j 15 k a 8 b / 112. p 8 q 80p /8 q m 4 n 8 72m \ n = x 5 y 4 144x 10 y 12 piral Review 115. olve: 116. Factor: 117. implify: 118. Factor: -(4x + 2) 4(x ) = 0 25x 2-16y 2 5m 8 n 60 4m 7 n 12p 2 p Alg2 - Radicals ~6~ NJTL.org
7 Adding and ubtracting Radicals - lass Work implify each expression x 27x 4 x 12x y + 4y 18y m 8 n 0 m mn kp 4 + 6p 0 k 16. 2r 4 8r 12r Alg2 - Radicals ~7~ NJTL.org
8 Adding and ubtracting Radicals - Homework implify each expression p 8 p p x x 8 6 x m 7 n = + 2m 7 n = a \ a \ y 8 4 4y x 6 x x piral Review 155. implify: 156. Factor: 157. Multiply: 158. implify: /0_`Ha` a`e 64p + 125q (a + 7)(2a 5) (-4r s -5 t 2 )(-5r 2 s -4 t) Alg2 - Radicals ~8~ NJTL.org
9 Multiplying Radicals - lass Work Multiply the following. Make sure answers are in simplest radical form (4 2)(2 ) 160. ( 5)(4 2) 161. ( 2 6)(4 12) (x 0 11) 16. (5 1x)( 2 2x) (2 + ) ( ) ( 5 6 7) Multiplying Radicals Homework Multiply the following. Make sure answers are in simplest radical form ( 6)(7 ) 175. (7y )(2 ) 176. ( )(5 12) ( 125) x( 5x) 179. (2 5 4 ) ( 2 6) x(2 15x ) piral Review 189. Factor: 190. Factor: 191. implify: 192. implify: 9m 2 + 0m x y 1 (a b -4 )(4a 4 b - ) /0d e 60de Alg2 - Radicals ~9~ NJTL.org
10 Rationalizing the Denominator - lass Work implify: / \ 8 \ / f 201. /6 0 /f f f f 7 0f Alg2 - Radicals ~10~ NJTL.org
11 Rationalizing the Denominator - Homework implify: \ \ 8 7 \ / f f f 7 / \6 / f 0 piral Review 217. implify: 218. Multiply: 219. Factor: 220. implify: g (2x 4)(x + 8) x 2 11x 4 4a 68 b 0 8 Alg2 - Radicals ~11~ NJTL.org
12 ube Roots - lass Work implify: x a 8 b / /? BE 226. A BU D H x 4 y \ z r 7 s 5 t mn 0 54m 0 n 4 p ab 64a b \ c /4 ube Roots - Homework implify: x a 7 b 0/ 27. / k l 28. m HT n j 4 k 8 m x 7 y \ z = 24. ab 56a 4 b 8 c x 0 z 4 40x 8 y 4 z piral Review 245. implify: 246. Multiply: 247. Multiply: 248. olve: x 8 x 68 (2a b)(4a 2 + 2ab + b 2 ) (4x 25y)(4x + 25y) 2(p 5) (p + 1) = 15 Alg2 - Radicals ~12~ NJTL.org
13 n th roots - lass Work implify: U x x /= U 25. x /9 y / z ? BH U u Hl v m n /\ x 7 y 8 z x 4 y z = x 16x 7 y /8 z /= T 260. m 4 n 80 p 0/ U 261. p x r + p /= x = y / U ? 267.? H / U FH 0R H U G H H I x 271. x k U 8 4? Alg2 - Radicals ~1~ NJTL.org
14 n th roots - Homework implify: U x x 89 U 277. x / y z /9 278.? B@ / U k H y U E a / b x 5 y /9 z // x 8 y 4 z 81x 0 y 4 z ab 64a / b 284. m r 5 /0 U y 1 /9 T n = p / I 8? H U 290. F T F 0G ? H x R U I? 295. =? 8R piral Review 296. Factor: 297. Multiply: 298. implify: 299. implify: 144p a 8 b 60 8 /0F 60 G Alg2 - Radicals ~14~ NJTL.org
15 Rational Exponents - lass Work implify: B U U H B T Write each expression without the radical m rs 0 t x 5 Write each expression using a single radical. 09. x H 10. a B b H c 11. e B Hf B g implify. Leave answers with positive exponents x 7 B H 1. U U a 6B H 16b`H l 16. c 2 5 /9 17.?? 18. I I T 19. z1 4 z 1 2z m 4 H Alg2 - Radicals ~15~ NJTL.org
16 Rational Exponents Homework implify: B H U B 25. / 80 6 B U H Write each expression without the radical p 28. r 4 s 8 t \ x 7 Write each expression using a single radical. 0. x B 1. a b H c 2. m B U n U Hp implify. Leave answers with positive exponents.. x 4 B H 4. y U U H 5. 4a 6B 6. 9b 6H T B 7. c 6 E l 8.??B 9. I I T 40. B F@ B B FF x /0 6 piral Review 42. implify: 4. Multiply: 44. implify: 45. Factor: g h g H h H (x + 4y)(x 4y) 2a 0 b y Alg2 - Radicals ~16~ NJTL.org
17 olving Radical Equations - lass Work olve each of the following equations x = a + 1 = 48. 2x = = 2 2t 50. 2p 4 B = m + 2 = 2m 52. 4x + 1 6x 9 = B H = 4m B H 54. t + 1 = t x + 4 = 2x + 2 Alg2 - Radicals ~17~ NJTL.org
18 olving Radical Equations - Homework olve each of the following equations. 56. g = x 1 = m = = 2 6 4b x 2 B = y + 5 = 2y x + 2 8x 7 = B = m B 64. t + 4 t = x + = x + 1 piral Review 66. implify: 67. Multiply: 68. Multiply: 69. implify: g (2x y)(4x y) 2 5 m 60 n 68 4 h ~ B Alg2 - Radicals ~18~ NJTL.org
19 omplex Numbers - lass Work implify using i. 70. i 4i 5i 71. 2i 4i 6i 8i 72. i 5i i 7. i i 7i i 74. 2i 2i 2i 75. 6i i i i 76. i i i \8 79. i i i x 5 14x \ 86. 0p 4 10p b a x 7 y \ m 4 n a 0 b x = y /0 Alg2 - Radicals ~19~ NJTL.org
20 omplex Numbers - Homework implify using i. 94. i i i 95. 4i 2i 9i i 96. i i 2i 97. i 4i i 5i 98. 2i 5i 7i 99. i i 5i 7i 400. i / i i \0 40. i i / 405. i i / i m 4m x 7 125x b = a x y r / x m \ n a 7 b /4 piral Review 421. Multiply: 422. Multiply: 42. Factor: 424. implify: (p + q)(9p 2 pq + q 2 ) 4x y(x 4 y 1) 64x + 27y ƒ ƒ H H Alg2 - Radicals ~20~ NJTL.org
21 Adding, ubtracting, and Multiplying omplex Numbers - lass Work implify: i 4 + i i + 2 i 427. i 5 i i + 5 i i 2 2i 40. 2i i i 42. 2i 6 + i 4. 4i i i i 4 + i i 2 2i i 1 i 48. i + i 49. 2i i i 1 i i ( 6 + i) 0 Alg2 - Radicals ~21~ NJTL.org
22 Adding, ubtracting, and Multiplying omplex Numbers - Homework implify: i + 2 i i 5i i i i + 4 9i i 5 i i 8 + 2i i + i i + + 2i i i 4 i 45. 4i + 2i 454. i 1 i i 8 + 2i i 4 9i i 5 i i 2 7i i ( 7 + 2i) 0 piral Review 461. Multiply: 462. Multiply: 46. Work out: 464. implify: (4q )(q 2 q 8) -2x 2 (y + z) (x ) ƒ ~ B Alg2 - Radicals ~22~ NJTL.org
23 Dividing omplex Numbers - lass Work implify f / \ / /68 / f f 476. \ / f f 482. /9 \ f Alg2 - Radicals ~2~ NJTL.org
24 Dividing omplex Numbers - Homework implify \ \ f = 8 f f f 0 7 f / 6 8 f / 6 4 / f / f 4 0 f / f 8 piral Review 505. Factor: 506. Multiply: 507. Multiply: 508. implify: 6m 2 19m 7 (xy 1)(xy + 1) (2x y)(4x 2 + 2xy + y 2 ) ~ g h B Alg2 - Radicals ~24~ NJTL.org
25 Radicals Answer Key Alg2 - Radicals ~25~ NJTL.org
26 Alg2 - Radicals ~26~ NJTL.org
27 Not a real number Not a real number 2. / Not a real number 0. b x 2 2. y 8. m 5 4. p Alg2 - Radicals ~27~ NJTL.org
28 5. /0? 6. AT 7 7. /8 8. D \ F l 9. GBH I@ / / \ a x m t x P ? E I BB 6. QB R (m 1)(9m 2 + m + 1) 66. x 8x 2 y + xy + 4xy 2 2y GH F 68. (x + )(2x 5) c Not a real number a x 0 y 8 5x 8. 64m 4 n r 4 s r pq r g h \ 6g x y a 8 y 0a x /8 y / a \ b 0 6ab 91. 0m 4 n m 8 m p 4 5p x n rs p 0 q r 0 2r x /9 y a 0 b \ c 8 ab Alg2 - Radicals ~28~ NJTL.org
29 g 8 h j /4 k 0 jk ab \ ab p 5 q /\ 5pq m \ n \ 2m x x y / x = 8 = x 4y 5x + 4y m 9 n 118. p(4p 1) x y 0 2y 14. 5m n m 15. 4p 0 k 16. 5r 0 2r 6r 0 r p p x 0 x m 8 n a 7 a y y 8y y x I ? E 156. (4p + 5q)(16p 2 20pq + 25p 2 ) a 2 a RU x l x x y x x x + 15x Alg2 - Radicals ~29~ NJTL.org
30 (m + 5) (xy 1)(9x 2 y 2 + xy + 1) 191. /0dT e T a \ / f 7 8/ f 8 0 \ / \ 8 / /9 0 0/ / \ 8 0 / / d e 0=f 4 / /9f x 2 + 4x (x 1)(x + 4) e@ d l x ab AU D E xy 0 xyz r 0 s 8 t mn 8 p 0 6m 0 n a 0 b 8 c 4 a 0 bc x 26. 9a 2 b / k m l 28. n BB jk jm x 0 y 0 z 0 5yz a 0 b 0 c 7ac x 8 yz 5yz a b x 2 625y p = Not a real number x x x 0 y 8 z ? 4 Alg2 - Radicals ~0~ NJTL.org
31 255. uu U u n m n 257. x 27x 0 y 8 z x yz 0 y x 0 y 8 z 4 x 0 yz n 4 p 8 T m 4 n p 262. (2x 1) (r + p) x 2 y U / x r U FH G 269. H I U I xH 0\k U 04? ? 27. Not a real number x 276. x x yz ? 7 U 279. k k y T ab 8 E a \ b x 0 y 0 z 0 7xy 0 z x 8 y z 7 x 0 z a 8 b a 8 b annot be simplified 285. (2r 5) (2y 1) np 0 T n ? H I 8? 289. U FH F T 0G 87? 8? 09R x R U 68 /7I 0I ? RU R 296. (12p 1)(12p + 1) a 9 b - 6 G H 299. /44F H / 70 / 0. =/ m B H 07. r B s H t 08. x l 09. x ab 0 c 8 BH e 7 f 4 g x 1. 24y B 14. /70d H d H eh /0 / A 17. 5x B 18. y T B 19. ˆ BH ˆ m 6 Alg2 - Radicals ~1~ NJTL.org
32 / p U H 28. r st T 29. 2x H ab 4 c 7 Hw 2. m 4 n 9 p /. x 2 4. y 2 H 5. 4d d 6. 0/=\ e U 7. A 8. x 9. y T 40. F T BH 41. F / =? l 42. 8e d 4. 9x 2 4y /7dE e B@ 45. (1 2y)(1 + 2y + 4y 2 ) 46. x = a = x = t = p = m = x = 5 5. m = No solution 55. x = g = x = m = =/ b = / x = No real solution 62. x = 6. m = t = x = 1 d(d f /) 66. ea 67. 8x 2 10xy + y =/ F E G BH i i i i i 79. i 80. i i x = p i 88. 6ib ai x 8 y 8 i 2y 91. 6m 0 ni 2n 92. 4a b 8 i 9. 5x 4 y 6 i 94. 9i Alg2 - Radicals ~2~ NJTL.org
33 i i i i i 407. i i m x i b 4 i 415. a 8 i x 0 y 8 i x r 6 i xi x m 8 ni 6mn a 8 b \ i p + q x 7 y 2-4x y 42. (4x + y)(16x 2 12xy + 9y 2 ) 424. I? i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i q 15q 2 2q x 2 y 2x 2 z 46. x 9x x 27?D 464. I(A f /) i i \ i f 4 Alg2 - Radicals ~~ NJTL.org
34 f 8 / f / f = i /6 0 /4 f 480. / \6 /9 /4 f = 482. / /5 / f \ i i i 491. \ i 49. / f = 494. /\ 495. / 6 = / f// f / f \ / 6/ 6 /\ / f 07 6/ f / f f /6/\ / (m + 1)(2m 7) x 2 y x y 508. A(ef/) dd Alg2 - Radicals ~4~ NJTL.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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