content.njctl.orgcontent.njctl.org/.../radicals-cwhw-2014-01-09.docx · Web viewGraph the following equations by hand. State the domain and range of each using interval notation

Graphing Square Roots - Class WorkGraph the following equations by hand. State the domain and range of each using interval notation.

1. y=−√x+2 2. f ( x )=√−3 x−1

3. y=√−x+3 4.g ( x )=−2√x−1

5. y=−√x+2+4 6. h ( x )=√−2 x−4−3

7. y=√3−x+2 8. y=√4 x−8−1

Alg2 - Radicals ~1~ NJCTL.org

Graphing Square Roots - HomeworkGraph the following equations by hand. State the domain and range of each using interval notation.

9. y=√−x+2 10. f ( x )=√−12x

11. y=−√x−4 12. g ( x )=−2√x+3−1

13. y=−12 √x+3 14. h ( x )=√3 x+6−2

15. y=√4−2x+3 16. y=−√3−3 x−4


Working with Square Roots - Class WorkSimplify each square root.

17. √25 18. √64 19. −√81 20. √−81

21. 21√ 2549 22. √−16121

23. √ 36144 24. −12√ 25100

25. −4√64 26. 10√81 27. −3√25 28. √16

29. 4 √−4 30. √b24 31. √ x4 32. √ y6

33. √m18 34. √ p10 35. √ 144x6 36. √ c1436

37. √ 169d8 38. √ 49m18 39. √ n244 40. √ y1216


Working with Square Roots - HomeworkSimplify each square root.

41. √289 42. −√400 43. √36 44. 3√361

45. √−10000 46. √ 25225 47. √ 49196 48. −12√ 81400

49. −2√ 3664 50. 5√9 51. −3√196 52. −7√49

53. −10√169 54. √a6 55. √ x8 56. √m10

57. √ t12 58. √ x4 59. √ h216 60. √ 4x16

61. √ 25d12 62. √ 81y22 63. √ g269 64. √ r836

Spiral Review65. Factor: 66. Multiply: 67. Simplify: 68. Factor:


27m3 – 1 (x – 2y)(3x2 – 2xy + y) 25m3n7

5m7n5 2x2 – x + 5

Irrational Roots - Class Work

Put in simplest radical form:69. √50 70. −3√48 71. 4 √20 72. √8

73. −2√75 74. 10√300c4 75. √−125 76. 7√28

77. −5√63 78. −8√72 79. 12√16 80. −2√18

81. 3√24a6 82. −4√20x5 y6 83. 16√16m8n12

84. −24 √48 r 9 s2 85. −6√32 p2q10r4 86. 100√6g3h14

87. 5√64 x10 y6 88. −13√30a7 y2 89. −40x y2√40 x24 y16

90. −3a3b√96a9b3 91. 15m2n6√120m4n6


Irrational Roots - Homework

Put in simplest radical form:92. √96 93. −3√150 94. 4 √80 95. −2√24

96. −12√500 97. 4m2√108m3 98. −5√120 99. 3√147

100. 7√84 101. −4√320 p9 102. −8√20 x6 103. 40 √27

104. −√14n12 105. 2√30 r3 s8 106. −8√8 p4q10 r5

107. −20√16 x20 y2 108. 7√75a5b15 c6 109. −10√100g6h10

110. −5√36 j15 k5 111. 12√a3b15 112. −p3q5√80 p13q25

113. 9m4n3√72m7n8 114. −4 x5 y4√144 x10 y12


Spiral Review115. Solve: 116. Factor: 117. Simplify: 118. Factor:-3(4x + 2) – 4(x – 3) = 0 25x2 - 16y2 (−5m3n−2 ) (−4m6n5 ) 12p2 – 3pAdding and Subtracting Radicals - Class Work

Simplify each expression119. 15√11 – √11 120. √10 + 4√10 121. √5 - 3√5

122. 2√6 + 3√3 123. 3√7 + 2√7 124. -3√6 + 8

√6

125. 5√13 + 73√13 - 4√13 126. 5√3 - √2 - 3√3 127. √27+√3−3√48

128. 4 √8−2√12+4√32 129. 2√45−7 √20+3√80 130. 2√12 - 7√27

131. −4√24−3 √54 132. 4 x√27 x4−x √12 x4 133. 5√8 y5+4 y √18 y3


134. √36m3n2−m√mn2 135. −2√k p4+6 p2√k 136.

3√2r5−4 √8 r5−3√12 r5

Adding and Subtracting Radicals - HomeworkSimplify each expression137. 3√10+8√10 138. 9√7−3√7 139. √3+4 √3

140. 2√10−4 √9−8√10 141. 5√4+7√4+7√7 142. 3√3+9√3+2√3

143. 10√5−√3−8√5 144. 4 √5 + √20 145. √98 - 2√2

146. 5√3 + √48 147. 9√7 - 2√63 148. √27 + √75

149. −√ p3−p√ p 150. −4 x√ x3−6√ x5 151. 5√8m6n8+3√32m6n8


152. 2√3 a7+4 √27a7 153. −5√12 y3−4√4 y3 154. 4 √3 x−6 √3 x+5√12 x

Spiral Review155. Simplify: 156. Factor: 157. Multiply: 158. Simplify: 12x−2 y−4

48 x6 y−8 64p3 + 125q3 (3a + 7)(2a – 5) (-4r3s-5t2)(-5r2s-4t)

Multiplying Radicals - Class WorkMultiply the following. Make sure answers are in simplest radical form.159. (4√2)¿) 160. (3√5)(4√2) 161. (−2√6)¿

162. −8√3(3 x2√11) 163. (5√13x )(−2√2 x) 164. 8√11(2+3√3)

165. 5√6(¿√6+4√7)¿ 166. −9√10¿) 167. (4+5√3 ) (3−2√3 )

168. (5−6√5 ) (5−6√6 ) 169. (3+3√5 ) (5−4√6 ) 170. (2−√3 ) (1+√2 )

171. (2+5√6 )2 172. (7−5√10 )2 173. (4−3√3 ) (√2+√3 )

Multiplying Radicals – HomeworkMultiply the following. Make sure answers are in simplest radical form.174. (−√6)¿) 175. (7 y √3)(2√3) 176. (−3√3)¿

177. √5(3√125) 178. −5√10 x (√5 x) 179. −√3(2√5−4√3)

180. 4 √3 (¿√2−3√6)¿ 181. −√5 x¿) 182. (5−√2 ) (2√3−√5 )

183. (4+2√3 ) (3−√6 ) 184. (2√5−2√3 ) (2−4 √6 ) 185. (1+√7 )2


186. (3+√2 ) (1−√3 ) 187. (8−√6 )2 188. (1−2√3 ) (1+2√3 )

Spiral Review189. Factor: 190. Factor: 191. Simplify: 192. Simplify:

9m2 + 30m + 25 27x3y3 – 1 (3a3b-4)(4a4b-3) 125a3b

−25ab

Rationalizing the Denominator - Class Work

Simplify:

193. 3√6

194. 1√5

195. 32√6

196. 3√2√3

197. 73√7

198. 3√5√2

199. 1

2−√3200. √5

6+√5

201. 1−√21+2√2

202. 2+√34−√5

203. 4

3√2+2√5204.

3+√62+√5


Rationalizing the Denominator - Homework

Simplify:

205. √2√5

206. 6√3

207. 74 √3

208. 5√5√2

209. 7√36√7

210. −2√6

√2211.

12−3√2

212. √64+√3

213. 3−√33+2√3

214. 4+√61−√5

215. 4

7−√10216. √5−√3

5+√2


Spiral Review217. Simplify: 218. Multiply: 219. Factor: 220. Simplify:

a3b6

(2x – 4)(3x + 8) 3x2 – 11x – 4 (−4a−3b2 )3

Cube Roots - Class WorkSimplify:221. 3√−8 222. 3√64 223. 3√−27 x6 224. 3√125a3b12

225. 3√−1x18

226. 3√ c15d24 227. 3√1 228. 3√−216

229. 3√27 x4 y7 z2 230. 3√32r 6 s9 t 9

231. 5mn2 3√54m2n4 p6 232. 3ab 3√64a5b7 c14

Cube Roots - HomeworkSimplify:233. 3√−512 234. 3√343 235. 3√−8 x9 236. 3√729a6b21

237. 3√−1p9

238. 3√ j27k33 239. 3√8 240. 3√−125


241. 3√24 j 4 k3m 242. 3√625 x6 y7 z8

243. 3ab 3√56a4b3 c5 244. 6 x2 z4 3√40 x3 y 4 z5

Spiral Review245. Simplify: 246. Multiply: 247. Multiply: 248. Solve: 3 x3 (3 x−3 ) (2a – b)(4a2 + 2ab + b2) (4x – 25y)(4x + 25y) 2(p – 5) – 3(p + 1) = 15

nth roots - Class WorkSimplify:249. 4√−81 250. 5√−1 251. 4√625 x16 252. 6√64 x18

253. 5√−x10 y15 z20 254. 4√ x12256 255. 5√ e29f 30 256. 6√64m5n17

257. 4√27 x6 y3 z2 258. 4√48 x4 y5 z8 259. 4 x 4√16 x6 y13 z18 260. 7√−m4n32 p21

261. 5√ (p−3 )5 262. 3√ (2x−1 )6 263. 6√ (r+3 p )18 264. 4√16 x8 y16


265. 35√2

266. −x4√x2 267.

13√2 r2 268.

2 5√m25√n2

269. 6√ x2y 270. 2t3√5 t

271. 4√ p33 272. 5√ 34 x4

nth roots - HomeworkSimplify:273. 4√−16 274. 5√−32 275. 4√16 x20 276. 6√729x30

277. 5√−x15 y5 z10 278. 4√ x16

1296279. 5√ p24q35 280. 8√256a15b25

281. 4√112 x9 y10 z11 282. 7 x3 y 4 z5 4√81 x2 y 4 z6 283. −3ab3 6√64a15b32

284. 6√ (m+2 )3 285. 3√ (2 r−5 )12 286. 5√ (2 y−1 )10 287. 7√128n8 p14

288.4√ 2 y3 x2 289. 4

5√m3 290. 7√ m2n 291. 3√43√3 x2


292. 4√ 2 t 35 r 293. −35√2 y

294. 5 x4√8x3 295.

96√3 r

Spiral Review296. Factor: 297. Multiply: 298. Simplify: 299. Simplify:

144p2 – 1 √7 (√10−2 ) (−3a3b−2 )3 ( 12mn )−2

Rational Exponents - Class Work

Simplify:

300. (−32 )15 301. (4 )

52 302. (125 )

−43

303. (27 )−43 304. (−18 )

−13 305. (16 )

74

Write each expression without the radical.306. √16m 307. 3√27 r s2t 4 308. 4√81x9

Write each expression using a single radical.

309. x23 310. a

13 b

23 c 311. e

12 f

13 g

34

Simplify. Leave answers with positive exponents.

312. (4 x6 )12 313. (27 y 65)

53 314. (25a−1

2 )62


315. (16 b−23 )

−94 316. (c−2

5 )10 317. 5x

x34

318. y

y37

319. −z

14

z12 z

23

320. (25m4 )32

Rational Exponents – Homework

Simplify:

321. (−125 )13 322. (4 )

32 323. (16 )

−54

324. (−27 )13 325. (−132 )

−15 326. (4 )

−32

Write each expression without the radical.327. √81 p5 328. 3√r4 s3 t7 329. 4√16 x6

Write each expression using a single radical.

330. x13 331. a

16b

23 c 332. m

15 n

52 p

34

Simplify. Leave answers with positive exponents.

333. (x4 )12 334. ( y 45 )

52 335. 4 a

−13


336. (9b−27 )

144 337. (c−3

8 )49 338.

x

x14

339. y

y47

340. m16

m14m

13

341. (16 x12)−34

Spiral Review342. Simplify: 343. Multiply: 344. Simplify: 345. Factor:

3aba2

b2 (3x + 4y)(3x – 4y) (2a2b−4 )4 1 – 8y3

Solving Radical Equations - Class WorkSolve each of the following equations.346. 3√2x=24 347. 3√a+1=3 348. 4√2x=2

349. 10=2√3−2t 350. 3−(2 p−4 )13=2 351. √m+2=√2m

352. 3√4 x+1− 3√6 x−9=0 353. (8 )12= (4m )

12 354. √ t+1=√ t−1


355. √2x+4=√2 x+2

Solving Radical Equations - HomeworkSolve each of the following equations.356. √3g=12 357. 3√ x−1=4 358. 4√2m=3

359. 12=2√6−4b 360. 4−3 (5 x−2 )13=10 361. √4 y+5=√2 y−6

362. 3√5 x+2−3√8x−7=0 363. (6 )13=(3m)

13 364. √−t+4−√ t=−2


365. √ x+3=√ x+1

Spiral Review366. Simplify: 367. Multiply: 368. Multiply: 369. Simplify:

abcd+1

(2x – y)(4x – 3y) 3√2 (√5−√3 ) (−3m−2n−3 )4

Complex Numbers - Class Work

Simplify using i.370. 3 i ∙4 i ∙5 i 371. −2 i ∙4 i ∙−6 i ∙8 i 372. −i ∙5 i ∙−3i

373. i ∙−3 i ∙7 i ∙−i 374. 2 i ∙2i ∙−2 i 375. −6 i ∙3 i ∙−3i ∙i

376. i9 377. −i22 378. i73


379. −i25 380. i33 381. i46

382. √−16 ∙√−25 383. √−8 ∙√−10 384. √−45

385. √−4 x9 ∙√−14 x7 386. √−30 p4 ∙√−10 p2 387. √−48

388. √−36b4 389. √−8a2 390. √−32x6 y7

391. √−72m4n3 392. √−48a2b6 393. √−25 x8 y12

Complex Numbers - HomeworkSimplify using i.394. −i ∙3 i ∙3 i 395. −4 i ∙2i ∙−9 i ∙−i 396. 3 i ∙ i ∙2i

397. i ∙4 i ∙−i ∙−5 i 398. 2 i ∙5i ∙7 i 399. −i ∙−3 i ∙−5 i ∙−7 i

400. i10 401. i23 402. i72

403. −i42 404. −i15 405. i66


406. i19 407. −i93 408. √−9 ∙√−4

409. √−12∙√−75 410. √−81 411. √−4m∙√−4m

412. √−27 x6 ∙√−125 x2 413. √−64 414. √−121b8

415. √−18a6 416. √−48 x5 y6 417. √−16 r12

418. √−24 x3 419. √−96m7n3 420. √−32a6b14

Spiral Review421. Multiply: 422. Multiply: 423. Factor: 424. Simplify:

(3p + q)(9p2 – 3pq + q2) 4x3y(3x4y – 1) 64x3 + 27y3

xyx2

y2Adding, Subtracting, and Multiplying Complex Numbers - Class WorkSimplify:

425. (6+5 i )− (4+3 i ) 426. (−3+2 i )+(−2−i ) 427. (3−i )−(5−i )

428. (3+5 i )+(5−3 i ) 429. (7+4 i )−(−2−2i ) 430. (−3−2i )−(3−i )

431. 5 (4−2 i ) 432. 2 i (−6+ i) 433. −4 i (3−i )


434. −6 (−4+3 i ) 435. (6+5 i ) (4+3i ) 436. (7+4 i ) (−2−2 i )

437. (−2+9 i ) (1−i ) 438. (3−i ) (3+i ) 439. (−3−2i ) (3−i )

440. (8−3 i ) (1−i ) 441. (4−2i )2 442. (−6+ i)2

Adding, Subtracting, and Multiplying Complex Numbers - HomeworkSimplify:443. (−1+i )+(−2−i ) 444. (7−2i )−(−3−5 i ) 445. (2+3 i )+ (8+2 i )

446. (4+9 i )+(−4−9i ) 447. (10−7 i)−(5−3 i ) 448. (2+3 i )−(8+2 i )


449. (−2−i )−(−3+i ) 450. (7+2 i )+(3+2 i ) 451. −6 (5−6 i )

452. 2 i (4−3i ) 453. −4 i (−3+2 i ) 454. −i (1−i )

455. (2+3 i ) (8+2i ) 456. (4+9 i ) (−4−9 i ) 457. (10−7 i) (5−3i )

458. (−6−i ) (2−7 i ) 459. (6−3 i )2 460. (−7+2i)2

Spiral Review461. Multiply: 462. Multiply: 463. Work out: 464. Simplify:

(4q – 3)(q2 – 3q – 8) -2x2(3y + z) (x – 3)3

xc+1yd

Dividing Complex Numbers - Class WorkSimplify

465. 2i 466.

34 i 467. −23 i 468.

2+ ii


469. −45 i 470.

−12 i 471.

−75i 472.

−4−3 i2 i

473. 2

1−2 i 474. 3 i1−3 i 475.

1+4 i5+i 476.

7−2 i2−9 i

477. 2i1−i 478.

−32−i 479.

2−i3+i 480.

4−i3−2 i

481. −2−i3+i 482.

107−4 i 483.

5−3 i3+2 i 484.

9−3 i5−2 i

Dividing Complex Numbers - HomeworkSimplify

485. −53 i 486.

25i 487.

−47 i 488.

4−ii


489. 3i 490.

−4i 491.

57 i

492. 6+5 i2 i

493. 83+i 494.

2 i4−i 495.

2−i2+3i 496.

5−i4−3 i

497. 5

5−2 i 498. −3+2 i6+3 i 499.

1−3 i5+2 i 500.

1−4 i1−5 i

501. 2i3−i 502.

2+i4−3 i 503.

−1+4 i2+i 504.

5−2 i1+3 i

Spiral Review505. Factor: 506. Multiply: 507. Multiply: 508. Simplify:


6m2 – 19m – 7 (3xy – 1)(3xy + 1) (2x – y)(4x2 + 2xy + y2)

cdab+1

Radicals Answer Key

1.

2.

3.

4.

5.

6.


7.

8.

9.

10.

11.

12.


13.

14.

15.

16.

17. 518. 819. -920. Not a real number21. 1522. Not a real number

23.12

24. 625. -3226. 9027. -15


28. 429. Not a real number30. b12

31. x2

32. |y3|33. |m9|34. |p5|

35.12|x3|

36. |c7|6

37.13d4

38.7

|m9|

39. n12

2

40. y6

441. 1742. -2043. 644. 5745. -100

46.13

47.12

48.−275

49. −¿250. 1551. -4252. -4953. -13054. |a3|55. x4

56. |m6|57. t 6

58. x2

59.|h|4

60.2x8

61.5d6

62.9

|y11|

63. g13

3

64. r4

665. (3m – 1)(9m2 + 3m + 1)66. 3x3 – 8x2y + xy + 4xy2 – 2y2

67.5n2

m4

68. (x + 3)(2x – 5)69. 5√270. −12√371. 8√572. 2√273. −10√374. 100c2√375. Not a real number76. 14√777. −15√778. −48√279. 4880. −6√281. 6|a3|√682. −8 x2|y3|√5 x83. 64m4n6

84. −96r 4|s|√3 r85. −24|pq5|r2√286. 100 g|h7|√6g87. 40|x5 y3|88. −13a3|y|√30a89. −80 x13 y10√1090. −12a7b2√6 ab


91. 30m4|n9|92. 4 √693. −15√694. 16√595. −4√696. −120√597. 24m3√3m98. −10√3099. 21√3

100. 14√21101. −32 p4√5 p102. −16|x3|√5103. 120√3104. – n6√14105. 2 r s4√30106. −16 p2|q5|r2√2r107. −80 x10|y|108. 35a2b7|c3|√3ab109. −100|g3h5|110. −30 j14 k2√ jk111. 12ab7√ab112. −4 p9q17√5 pq113. 54m7n7√2m114. −48x5|x5|y10

115. x=38116. (5 x−4 y ) (5 x+4 y )117. 20m9n3

118. 3p(4p – 1)119. 14√11120. 5√10121. −2√5122. 2√6+3√3123. 5√7124. 5√6125. √13+7 3√13126. 2√3−√2127. −8√3

128. 24√2−4√3129. 4 √5130. −17√3131. −17√6132. 10 x3√3133. 22 y2√2 y134. 5m|n|√m135. 4 p2√k136. −5 r2√2 r−6 r2√3 r137. 11√10138. 6√7139. 5√3140. −12−6 √10141. 24+7√7142. 14√3143. 2√5−√3144. 6√5145. 5√2146. 9√3147. 3√7148. 8√3149. −2 p √ p150. −10 x2√ x151. 22|m3|n4√2152. 14a6√3a153. −10 y √3 y−8 y√ y154. 8√3 x

155. y4

4 x8

156. (4p + 5q)(16p2 – 20pq + 25p2)157. 6a2 – a – 35

158.20 r5t 3

s9

159. 8√6160. 12√10161. −48√2162. −24 x2√33163. −10|x|√26164. 16√11+24√33


165. 30+20√7166. −135√2+54√70167. −18+7√3168. 25−30√5−30√6+36√30169. 15+15√5−12√6−12√30170. 2−√3+2√2−√6171. 154+20√6172. 299−70√10173. 4 √2−3√6+4 √3−9174. −21√2175. 42y176. -90177. 75178. −25|x|√2179. 12−2√15180. 4 √6−36√2181. −10|x|√3 x+√15x182. 10√3−5√5−2√6+√10183. 12+6√3−4√6−6√2184. 4 √5−4 √3−8√30+24√2185. 8+2√7186. 3+√2−3√3−√6187. 70−16√6188. -11189. (3m + 5)2

190. (3xy – 1)(9x2y2 + 3xy + 1)

191. 12a7

b7

192. -5a2

193. √62

194. √55

195. √64

196. √6

197. √73

198. 3√102

199. 2+√3

200. −5+6√531

201. −5+3√27

202. −8−4 √3−2√5−√15203. −6√2+4 √5204. −6−2√6+3√5+√30

205. √105

206. 2√3

207. 7√312

208. 5√102

209. √216

210. −2√3

211. −17

−3√214

212. 4 √6−3√213

213. −5+3√3

214. −1−√64

−√5−√304

215. 28+4 √1039

216. 5√5−5√3−√10+√623

217. 2ab

218. 6x2 + 4x – 32219. (3x – 1)(x + 4)

220. −64b6

a9

221. -2222. 4223. -3x2

224. 5ab4

225. −1x6


226. c5

d8

227. 1228. -6229. 3 x y2 3√xy z2230. 2 r2 s3 t 3 3√4231. 15mn3 p2 3√6m2n232. 12a2b3 c4 3√a2b c2233. -8234. 7235. -2x3

236. 9a2b7

237. −1p3

238. j9

k11

239. 2240. -5241. 2 jk 3√3 jm242. 5 x2 y2 z2 3√5 y z2243. 6a2b2c 3√7 ac2244. 12 x3 y z5 3√5 y z2245. 9246. 8a3 – b3

247. 16x2 – 625y2

248. p = -28249. Not a real number250. -1251. 5x4

252. 2|x3|253. −x2 y3 z4

254. |x3|4

255. e5 5√e4f 6

256. 2n2 6√m5n5257. x 4√27 x2 y3 z2258. 2|x| y z2 4√3 y

259. 8 x2 y3 z4 4√x2 y z2260. −n4 p3 7√m4n4261. p – 3262. (2x – 1)2

263. (r + 3p)3

264. 2x2y4

265. 35√162

266. −4√ x2267. 2r

268. 25√m2n3n

269. 6√x2 y5y

270. 23√25 t 25

271. 4√27 p33

272. 5√24 x2x

273. Not a real number274. -2275. 2|x5|276. 3x5

277. –x3yz2

278. x4

6

279. p4 5√ p4q7

280. 2ab3 8√a7b281. 2 x2 y2 z2 4√7 x y2 z3282. 63 x3 y5 z6 4√ x2 z2283. −6a3b8 6√a3b2284. Cannot be simplified285. (2r – 5)4

286. (2y – 1)2

287. 2n p2 7√n

288. 4√54 x2 y3 x


289. 55√m2m

290. 7√64mn62n

291. 3√36 x3x

292. 4√250 r3 t 35 r

293. −35√16 y 42 y

294. 54√2 x2

295. 36√243 r5r

296. (12p – 1)(12p + 1)297. √70−2√7298. -27a9b-6

299. n2

144m2

300. -2301. 32

302. 1625

303. 181

304. -2305. 128

306. 4m12

307. 3 r13 s

23 t43

308. 3 x94

309. 3√ x2310. 3√ab2 c3311. 4 12√e6 f 4 g9312. 4x3

313. 243y3

314. 15625a12

a2

315. b32

512

316. 1c4

317. 5 x14

318. y47

319. −z112

z320. 125m6

321. -5322. 8

323. 132

324. -3325. -2

326. 18

327. 9 p52

328. r43 s t

73

329. 2 x32

330. 3√ x331. 6√ab4 c6332. 20√m4n50 p15333. x2

334. y2

335. 4 a23

a

336. 2187b

337. c56

c

338. x34

339. y37


340. m712

m

341. 18 x9

342. 3ba

343. 9x2 – 4y2

344.16a8

b16

345. (1 – 2y)(1 + 2y + 4y2)346. x = 32347. a = 26348. x = 8349. t = -11

350. p=52351. m = 2352. x = 5353. m = 2354. No solution355. x = 0356. g = 48357. x = 65

358. m=812

359. b=−152

360. x=−65

361. No real solution362. x = 3363. m = 2364. t = 4365. x = 1

366. a(d+1)bc

367. 8x2 – 10xy + 3y2

368. 3√10−3√6

369. 81m8n12

370. -60i

371. 384372. -15i373. 21374. 8i375. 54376. i377. 1378. i379. –i380. i381. -1382. -20383. −4√5384. 3 i√5385. −2 x8√14386. −10|p3|√3387. 4 i√3388. 6ib2

389. 2ai√2390. 4|x3 y3|i √2 y391. 6m2∋√2n392. 4 a|b3|i√3393. 5x4y6i394. 9i395. -72396. -6i397. 20398. -70i399. 105400. -1401. –i402. 1403. 1404. i405. -1406. –i407. –i408. -12409. −6√15410. 9i


411. −4|m|412. −15 x4√15413. 8i414. 11b4i415. 3a3 i √2416. 4 x2|y3|i√3 x417. 4r6i418. 2 xi√3 x419. 4m3∋√6mn420. 4|a3b7|i√2421. 27p3 + q3

422. 12x7y2- 4x3y423. (4x + 3y)(16x2 – 12xy + 9y2)

424. yx

425. 2 + 2i426. -5 + i427. -2428. 8 + 2i429. 9 + 6i430. -6 – i431. 20 – 10i432. -2 – 12i433. -4 – 12i434. 24 – 18i435. 9 + 38i436. -6 – 22i437. 7 + 11i 438. 10439. -11 – 3i440. 5 – 11i 441. 12 – 16i442. 35 – 12i443. -3444. 10 + 3i445. 10 + 5i446. 0447. 5 – 4i448. -6 + i449. 1 – 2i450. 10 + 4i

451. -30 + 36i452. 6 + 8i453. 8 + 12i454. -1 – i455. 10 + 28i456. 65 – 72i457. 29 – 65i458. -19 + 42i459. 27 – 36i460. 45 – 28i461. 4q3 – 15q2 – 23q + 24462. -6x2y – 2x2z463. x3 – 9x2 + 27x – 27

464. xd

y (c+1)465. -2i

466. −3 i4

467. 2i3

468. 1 – 2i

469. 4 i5

470.i2

471. 7 i5

472. −32

+2i

473. 2+4 i5

474. −9+3 i10

475. 9+19 i26

476. 32+59i85

477. -1 + i

478. −6−3i5

479. 1−i2


480. 14+5 i13

481. −7−i10

482. 14+8 i13

483. 9−19 i13

484. 5+3 i29

485. 5i3

486. −2i5

487. 4 i7

488. -1 – 4i489. -3i490. 4i

491. −5 i7

492. 52−3 i

493. 12−4 i5

494. −2+8 i17

495. 1−8 i13

496. 23+11 i25

497. 25+10 i29

498. −4+7 i15

499. −1−17 i29

500. 21+ i26

501. −1+3i5

502. 1+2i5

503. 2+9 i5

504. −1−17 i10

505. (3m + 1)(2m – 7)506. 9x2y2 – 1507. 8x3 – y3

508. c (b+1)ad


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content.njctl.orgcontent.njctl.org/.../radicals-cwhw-2014-01-09.docx · Web viewGraph the following equations by hand. State the domain and range of each using interval notation