Graphing)Square)Roots)2)Class)Work)macintodd.net/wp-content/uploads/2015/08/Unit-5-HW... · 2020. 2. 16. · Alg2&!Radicals! ~3~! NJCTL.org! Working)with)Square)Roots)2)Class)Work)

Alg2 -‐ Radicals ~1~ NJCTL.org

Graphing Square Roots - Class Work Graph the following equations by hand. State the domain and range of each using interval notation. 1. 𝑦 = − 𝑥 + 2 2. 𝑓 𝑥 = −3𝑥 − 1 3. 𝑦 = −𝑥 + 3 4. 𝑔 𝑥 = −2 𝑥 − 1 5. 𝑦 = − 𝑥 + 2 + 4 6. ℎ 𝑥 = −2𝑥 − 4 − 3 7. 𝑦 = 3 − 𝑥 + 2 8. 𝑦 = 4𝑥 − 8 − 1


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

9. 𝑦 = −𝑥 + 2 10. 𝑓 𝑥 = − /0𝑥

11. 𝑦 = − 𝑥 − 4 12. 𝑔 𝑥 = −2 𝑥 + 3 − 1 13. 𝑦 = − /

0𝑥 + 3 14. ℎ 𝑥 = 3𝑥 + 6 − 2

15. 𝑦 = 4 − 2𝑥 + 3 16. 𝑦 = − 3 − 3𝑥 − 4


Working with Square Roots - Class Work Simplify each square root. 17. 25 18. 64 19. − 81 20. −81

21. 21 0345 22. 6/7

/0/ 23. 87

/44 24. −12 03

/99

25. −4 64 26. 10 81 27. −3 25 28. 16 29. 4 −4 30. 𝑏04 31. 𝑥4 32. 𝑦7

33. 𝑚/= 34. 𝑝/9 35. /44?@ 36. ABC

87

37. /75DE 38. 45

FBE 39. GHC

4 40. IBH

/7


Working with Square Roots - Homework Simplify each square root. 41. 289 42. − 400 43. 36 44. 3 361

45. −10000 46. 03003 47. 45

/57 48. −12 =/

499

49. −2 8774 50. 5 9 51. −3 196 52. −7 49

53. −10 169 54. a7 55. x= 56. m/9

57. t/0 58. x4 59. PH

/7 60. 4

?B@

61. 03DBH 62. =/

IHH 63. QH@

5 64. RE

87

Spiral Review 65. Factor: 66. Multiply: 67. Simplify: 68. Factor: 27m3 – 1 (x – 2y)(3x2 – 2xy + y) 03F

SGT

3FTGU 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 24𝑎7 82. −4 20𝑥3𝑦7 83. 16 16𝑚=𝑛/0 84. −24 48𝑟5𝑠0 85. −6 32𝑝0𝑞/9𝑟4 86. 100 6𝑔8ℎ/4 87. 5 64𝑥/9𝑦7 88. −13 30𝑎\𝑦0 89. −40𝑥𝑦0 40𝑥04𝑦/7 90. −3𝑎8𝑏 96𝑎5𝑏8 91. 15𝑚0𝑛7 120𝑚4𝑛7


Irrational Roots - Homework Put in simplest radical form: 92. 96 93. −3 150 94. 4 80 95. −2 24 96. −12 500 97. 4𝑚0 108𝑚8 98. −5 120 99. 3 147 100. 7 84 101. −4 320𝑝5 102. −8 20𝑥7 103. 40 27 104. − 14𝑛/0 105. 2 30𝑟8𝑠= 106. −8 8𝑝4𝑞/9𝑟3

107. −20 16𝑥09𝑦0 108. 7 75𝑎3𝑏/3𝑐7 109. −10 100𝑔6ℎ10

110. −5 36𝑗15𝑘5 111. 12 𝑎8𝑏/3 112. −𝑝8𝑞3 80𝑝/8𝑞03 113. 9𝑚4𝑛8 72𝑚\𝑛= 114. −4𝑥5𝑦4 144𝑥10𝑦12 Spiral Review 115. Solve: 116. Factor: 117. Simplify: 118. Factor: -3(4x + 2) – 4(x – 3) = 0 25x2 - 16y2 −5𝑚8𝑛60 −4𝑚7𝑛3 12p2 – 3p


Adding and Subtracting Radicals - Class Work Simplify each expression 119. 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 + 7 13S - 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. 4𝑥 27𝑥4 − 𝑥 12𝑥4 133. 5 8𝑦3 + 4𝑦 18𝑦8 134. 36𝑚8𝑛0 − 𝑚 𝑚𝑛0 135. −2 𝑘𝑝4 + 6𝑝0 𝑘 136. 3 2𝑟3 − 4 8𝑟3 − 3 12𝑟3


Adding and Subtracting Radicals - Homework Simplify each expression 137. 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. − 𝑝8 − 𝑝 𝑝 150. −4𝑥 𝑥8 − 6 𝑥3 151. 5 8𝑚7𝑛= + 3 32𝑚7𝑛= 152. 2 3𝑎\ + 4 27𝑎\ 153. −5 12𝑦8 − 4 4𝑦8 154. 4 3𝑥 − 6 3𝑥 + 5 12𝑥 Spiral Review 155. Simplify: 156. Factor: 157. Multiply: 158. Simplify: /0_`Ha`C

4=_@a`E 64p3 + 125q3 (3a + 7)(2a – 5) (-4r3s-5t2)(-5r2s-4t)


Multiplying Radicals - Class Work Multiply the following. Make sure answers are in simplest radical form. 159. (4 2)(2 3) 160. (3 5)(4 2) 161. (−2 6)(4 12) 162. −8 3(3𝑥0 11) 163. (5 13𝑥)(−2 2𝑥) 164. 8 11(2 + 3 3) 165. 5 6( 6 + 4 7) 166. −9 10(3 5 − 6 7) 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

0 172. 7 − 5 10

0 173. 4 − 3 3 2 + 3

Multiplying Radicals – Homework Multiply the following. Make sure answers are in simplest radical form. 174. (− 6)(7 3) 175. (7𝑦 3)(2 3) 176. (−3 3)(5 12) 177. 5(3 125) 178. −5 10𝑥( 5𝑥) 179. − 3(2 5 − 4 3) 180. 4 3( 2 − 3 6) 181. − 5𝑥(2 15𝑥 − 3) 182. 5 − 2 2 3 − 5 183. 4 + 2 3 3 − 6 184. 2 5 − 2 3 2 − 4 6 185. 1 + 7

0

186. 3 + 2 1 − 3 187. 8 − 6

0 188. 1 − 2 3 1 + 2 3

Spiral Review 189. Factor: 190. Factor: 191. Simplify: 192. Simplify: 9m2 + 30m + 25 27x3y3 – 1 (3a3b-4)(4a4b-3) /03d

Se603de


Rationalizing the Denominator - Class Work Simplify:

193. 87 194.

/3 195.

80 7

196. 8 08

197. \8 \

198. 8 30 199.

/06 8

200. 3

7f 3

201. /6 0/f0 0

202. 0f 846 3

203. 4

8 0f0 3 204.

8f 70f 3


Rationalizing the Denominator - Homework Simplify:

205. 03 206.

78 207.

\4 8

208. 3 30

209. \ 87 \

210. 60 7

0 211.

/068 0

212. 7

4f 8

213. 86 88f0 8

214. 4f 7/6 3

215. 4

\6 /9 216.

36 83f 0

Spiral Review 217. Simplify: 218. Multiply: 219. Factor: 220. Simplify:

gSh@

(2x – 4)(3x + 8) 3x2 – 11x – 4 −4𝑎68𝑏0 8


Cube Roots - Class Work Simplify: 221. −8S 222. 64S 223. −27x7S 224. 125𝑎8𝑏/0S

225. − /?BE

S 226. ABU

DHCS

227. 1S 228. −216S

229. 27𝑥4𝑦\𝑧0S 230. 32𝑟7𝑠5𝑡5S 231. 5𝑚𝑛0 54𝑚0𝑛4𝑝7S 232. 3𝑎𝑏 64𝑎3𝑏\𝑐/4S Cube Roots - Homework Simplify: 233. −512S 234. 343S 235. −8x5S 236. 729𝑎7𝑏0/S

237. − /kl

S 238. mHT

nSSS

239. 8S 240. −125S

241. 24j4k8mS 242. 625x7y\z=S 243. 3𝑎𝑏 56a4b8c3S 244. 6x0z4 40x8y4z3S Spiral Review 245. Simplify: 246. Multiply: 247. Multiply: 248. Solve: 3𝑥8 3𝑥68 (2a – b)(4a2 + 2ab + b2) (4x – 25y)(4x + 25y) 2(p – 5) – 3(p + 1) = 15


nth roots - Class Work Simplify: 249. −81C 250. −1U 251. 625𝑥/7C 252. 64𝑥/=@

253. −𝑥/9𝑦/3𝑧09U 254. ?BH

037

C 255. uHl

vSwU 256. 64𝑚3𝑛/\@

257. 27𝑥7𝑦8𝑧0C 258. 48𝑥4𝑦3𝑧=C 259. 4𝑥 16𝑥7𝑦/8𝑧/=C 260. −𝑚4𝑛80𝑝0/T 261. 𝑝 − 3 3U 262. 2𝑥 − 1 7S 263. 𝑟 + 3𝑝 /=@ 264. 16𝑥=𝑦/7C

265. 80U 266.

6??HC 267.

/0RHS 268.

0 FHU

GHU

269. ?H

I@

270. 0x3xS 271.

kS

8

C 272.

84?C

U


nth roots - Homework Simplify: 273. −16C 274. −32U 275. 16𝑥09C 276. 729𝑥89@

277. −𝑥/3𝑦3𝑧/9U 278. ?B@

/057

C 279. kHC

ySUU 280. 256𝑎/3𝑏03E

281. 112x5y/9z//C 282. 7x8y4z3 81x0y4z7C 283. −3𝑎𝑏8 64𝑎/3𝑏80@ 284. 𝑚 + 2 8@ 285. 2𝑟 − 5 /0S 286. 2𝑦 − 1 /9U 287. 128𝑛=𝑝/4T

288. 0I8?H

C 289.

4

FSU 290. F0G

T 291.

4S

8?HS

292. 0xS

3R

C 293.

680IU 294.

3?=?SC 295.

58R@

Spiral Review 296. Factor: 297. Multiply: 298. Simplify: 299. Simplify: 144p2 – 1 7 10 − 2 −3𝑎8𝑏60 8 /0F

G

60


Rational Exponents - Class Work Simplify: 300. −32

BU 301. 4

UH 302. 125 6CS

303. 27 6CS 304. − /=

6BS 305. 16TC

Write each expression without the radical. 306. 16m 307. 27rs0t4S 308. 81𝑥5C Write each expression using a single radical. 309. 𝑥

HS 310. 𝑎

BS𝑏

HS𝑐 311. 𝑒

BH𝑓

BS𝑔

SC

Simplify. Leave answers with positive exponents.

312. 4𝑥7BH 313. 27𝑦

@U

US 314. 25𝑎6

BH

@H

315. 16𝑏`HS

6lC 316. 𝑐

−25

/9 317.

3?

?SC

318. I

IST 319. − 𝑧

14

𝑧12𝑧23 320. 25𝑚4

SH


Rational Exponents – Homework Simplify: 321. −125

BS 322. 4

SH 323. 16 6UC

324. −27BS 325. − /

80

6BU 326. 4 6SH

Write each expression without the radical. 327. 81p3 328. r4s8t\S 329. 16𝑥7C Write each expression using a single radical. 330. 𝑥

BS 331. 𝑎

B@𝑏

HS𝑐 332. 𝑚

BU𝑛

UH𝑝

SC

Simplify. Leave answers with positive exponents.

333. 𝑥4BH 334. 𝑦

CU

UH 335. 4𝑎6

BS

336. 9𝑏6HT

BCC 337. 𝑐6

SE

Cl 338. ?

?BC

339. IICT 340. F

B@

FBCF

BS 341. 16𝑥/0 6SC

Spiral Review 342. Simplify: 343. Multiply: 344. Simplify: 345. Factor:

SghgH

hH

(3x + 4y)(3x – 4y) 2𝑎0𝑏64 4 1 – 8y3


Solving Radical Equations - Class Work Solve each of the following equations. 346. 3 2𝑥 = 24 347. 𝑎 + 1S = 3 348. 2xC = 2 349. 10 = 2 3 − 2𝑡 350. 3 − 2𝑝 − 4

BS = 2 351. 𝑚 + 2 = 2𝑚

352. 4x + 1S − 6x − 9S = 0 353. 8

BH = 4m

BH 354. 𝑡 + 1 = 𝑡 − 1

355. 2𝑥 + 4 = 2𝑥 + 2


Solving Radical Equations - Homework Solve each of the following equations. 356. 3𝑔 = 12 357. 𝑥 − 1S = 4 358. 2mC = 3 359. 12 = 2 6 − 4𝑏 360. 4 − 3 5𝑥 − 2

BS = 10 361. 4𝑦 + 5 = 2𝑦 − 6

362. 5x + 2S − 8x − 7S = 0 363. 6

BS = 3m

BS 364. −𝑡 + 4 − 𝑡 = −2

365. 𝑥 + 3 = 𝑥 + 1 Spiral Review 366. Simplify: 367. Multiply: 368. Multiply: 369. Simplify:

gh~

� � B (2x – y)(4x – 3y) 3 2 5 − 3 −3𝑚60𝑛68 4


Complex Numbers - Class Work Simplify using i. 370. 3𝑖 ∙ 4𝑖 ∙ 5𝑖 371. −2𝑖 ∙ 4𝑖 ∙ −6𝑖 ∙ 8𝑖 372. −𝑖 ∙ 5𝑖 ∙ −3𝑖 373. 𝑖 ∙ −3𝑖 ∙ 7𝑖 ∙ −𝑖 374. 2𝑖 ∙ 2𝑖 ∙ −2𝑖 375. −6𝑖 ∙ 3𝑖 ∙ −3𝑖 ∙ 𝑖 376. 𝑖5 377. −𝑖00 378. 𝑖\8 379. −𝑖03 380. 𝑖88 381. 𝑖47 382. −16 ∙ −25 383. −8 ∙ −10 384. −45 385. −4𝑥5 ∙ −14𝑥\ 386. −30𝑝4 ∙ −10𝑝0 387. −48 388. −36𝑏4 389. −8𝑎0 390. −32𝑥7𝑦\ 391. −72𝑚4𝑛8 392. −48𝑎0𝑏7 393. −25𝑥=𝑦/0


Complex Numbers - Homework Simplify using i. 394. −𝑖 ∙ 3𝑖 ∙ 3𝑖 395. −4𝑖 ∙ 2𝑖 ∙ −9𝑖 ∙ −𝑖 396. 3𝑖 ∙ 𝑖 ∙ 2𝑖 397. 𝑖 ∙ 4𝑖 ∙ −𝑖 ∙ −5𝑖 398. 2𝑖 ∙ 5𝑖 ∙ 7𝑖 399. −𝑖 ∙ −3𝑖 ∙ −5𝑖 ∙ −7𝑖 400. 𝑖/9 401. 𝑖08 402. 𝑖\0 403. −𝑖40 404. −𝑖/3 405. 𝑖77 406. 𝑖/5 407. −𝑖58 408. −9 ∙ −4 409. −12 ∙ −75 410. −81 411. −4𝑚 ∙ −4𝑚 412. −27𝑥7 ∙ −125𝑥0 413. −64 414. −121𝑏= 415. −18𝑎7 416. −48𝑥3𝑦7 417. −16𝑟/0 418. −24𝑥8 419. −96𝑚\𝑛8 420. −32𝑎7𝑏/4 Spiral Review 421. Multiply: 422. Multiply: 423. Factor: 424. Simplify:

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

�H


Adding, Subtracting, and Multiplying Complex Numbers - Class Work Simplify: 425. 6 + 5𝑖 − 4 + 3𝑖 426. −3 + 2𝑖 + −2 − 𝑖 427. 3 − 𝑖 − 5 − 𝑖 428. 3 + 5𝑖 + 5 − 3𝑖 429. 7 + 4𝑖 − −2 − 2𝑖 430. −3 − 2𝑖 − 3 − 𝑖 431. 5 4 − 2𝑖 432. 2𝑖 −6 + 𝑖 433. −4𝑖 3 − 𝑖 434. −6 −4 + 3𝑖 435. 6 + 5𝑖 4 + 3𝑖 436. 7 + 4𝑖 −2 − 2𝑖 437. −2 + 9𝑖 1 − 𝑖 438. 3 − 𝑖 3 + 𝑖 439. −3 − 2𝑖 3 − 𝑖 440. 8 − 3𝑖 1 − 𝑖 441. 4 − 2𝑖 0 442. (−6 + 𝑖)0


Adding, Subtracting, and Multiplying Complex Numbers - Homework Simplify: 443. −1 + 𝑖 + −2 − 𝑖 444. 7 − 2𝑖 − −3 − 5𝑖 445. 2 + 3𝑖 + 8 + 2𝑖 446. 4 + 9𝑖 + −4 − 9𝑖 447. 10 − 7𝑖 − 5 − 3𝑖 448. 2 + 3𝑖 − 8 + 2𝑖 449. −2 − 𝑖 − −3 + 𝑖 450. 7 + 2𝑖 + 3 + 2𝑖 451. −6 5 − 6𝑖 452. 2𝑖 4 − 3𝑖 453. −4𝑖 −3 + 2𝑖 454. −𝑖 1 − 𝑖 455. 2 + 3𝑖 8 + 2𝑖 456. 4 + 9𝑖 −4 − 9𝑖 457. 10 − 7𝑖 5 − 3𝑖 458. −6 − 𝑖 2 − 7𝑖 459. 6 − 3𝑖 0 460. (−7 + 2𝑖)0 Spiral Review 461. Multiply: 462. Multiply: 463. Work out: 464. Simplify:

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


Dividing Complex Numbers - Class Work Simplify

465. 0� 466.

84� 467. − 0

8� 468. 0f�

�

469. − 4

3� 470. − /

0� 471. − \

3� 472. 6468�

0�

473. 0

/60� 474. 8�

/68� 475. / f4�

3 f � 476. \60�

065�

477. 0�

/ 6 � 478. 68

0 6 � 479. 0 6 �

8 f � 480. 4 6 �

8 6 0�

481. 60 6 �

8 f � 482. /9

\ 6 4� 483. 3 6 8�

8 f 0� 484. 5 6 8�

3 6 0�


Dividing Complex Numbers - Homework Simplify 485. − 3

8� 486. 0

3� 487. 64

\� 488. 46�

�

489. 8

� 490. − 4

� 491. 3

\� 492. 7 f3 �

0�

493. =

8 f � 494. 0�

4 6 � 495. 0 6 �

0 f 8� 496. 3 6 �

4 6 8�

497. 3

3 6 0� 498. 68 f 0�

7 f 8� 499. / 6 8�

3 f 0� 500. / 6 4�

/ 6 3�

501. 0�

8 6 � 502. 0 f �

4 6 8� 503. 6/ f 4�

0 f � 504. 3 6 0�

/ f 8�

Spiral Review 505. Factor: 506. Multiply: 507. Multiply: 508. Simplify:

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

h � B


Radicals Answer Key

1. 2. 3. 4. 5. 6.


7. 8. 9. 10. 11. 12.


13. 14. 15. 16.

17. 5 18. 8 19. -‐9 20. Not a real number 21. 15 22. Not a real number

23. /0

24. 6 25. -‐32

26. 90 27. -‐15 28. 4 29. Not a real number 30. b12 31. x2 32. 𝑦8 33. 𝑚5 34. 𝑝3


35. /0?S

36. AT

7

37. /8DC

38. \Fl

39. GBH

0

40. I@

4

41. 17 42. -‐20 43. 6 44. 57 45. -‐100 46. /

8

47. /0

48. − 0\3

49. −2 50. 15 51. -‐42 52. -‐49 53. -‐130 54. 𝑎8 55. 𝑥4 56. 𝑚7 57. 𝑡7 58. 𝑥0 59. P

4

60. 0?E

61. 3D@

62. 5IBB

63. QBS

8

64. RC

7

65. (3m – 1)(9m2 + 3m + 1) 66. 3x3 – 8x2y + xy + 4xy2 – 2y2

67. 3GH

FC

68. (x + 3)(2x – 5) 69. 5 2

70. −12 3 71. 8 5 72. 2 2 73. −10 3 74. 100𝑐0 3 75. Not a real number 76. 14 7 77. −15 7 78. −48 2 79. 48 80. −6 2 81. 6 𝑎8 6 82. −8𝑥0 𝑦8 5𝑥 83. 64𝑚4𝑛7 84. −96𝑟4 𝑠 3𝑟 85. −24 𝑝𝑞3 𝑟0 2 86. 100𝑔 ℎ\ 6𝑔 87. 40 𝑥3𝑦8

88. −13𝑎8 𝑦 30𝑎 89. −80𝑥/8𝑦/9 10 90. −12𝑎\𝑏0 6𝑎𝑏 91. 30𝑚4 𝑛5 92. 4 6 93. −15 6 94. 16 5 95. −4 6 96. −120 5 97. 24𝑚8 3𝑚 98. −10 30 99. 21 3 100. 14 21 101. −32𝑝4 5𝑝 102. −16 𝑥8 5 103. 120 3 104. – 𝑛7 14 105. 2𝑟𝑠4 30 106. −16𝑝0 𝑞3 𝑟0 2𝑟 107. −80𝑥/9 𝑦 108. 35𝑎0𝑏\ 𝑐8 3𝑎𝑏


109. −100 𝑔8ℎ3

110. −30𝑗/4𝑘0 𝑗𝑘 111. 12𝑎𝑏\ 𝑎𝑏 112. −4𝑝5𝑞/\ 5𝑝𝑞 113. 54𝑚\𝑛\ 2𝑚 114. −48𝑥3 𝑥3 𝑦/9

115. 𝑥 = 8=

116. 5𝑥 − 4𝑦 5𝑥 + 4𝑦 117. 20m9n3 118. 3p(4p – 1) 119. 14 11 120. 5 10 121. −2 5 122. 2 6 + 3 3 123. 5 7 124. 5 6 125. 13 + 7 13S 126. 2 3 − 2 127. −8 3 128. 24 2 − 4 3 129. 4 5 130. −17 3 131. −17 6 132. 10𝑥8 3 133. 22𝑦0 2𝑦 134. 5𝑚 𝑛 𝑚 135. 4𝑝0 𝑘 136. −5𝑟0 2𝑟 − 6𝑟0 3𝑟 137. 11 10 138. 6 7 139. 5 3 140. −12 − 6 10 141. 24 + 7 7 142. 14 3 143. 2 5 − 3 144. 6 5 145. 5 2 146. 9 3 147. 3 7

148. 8 3 149. −2𝑝 𝑝 150. −10𝑥0 𝑥 151. 22 𝑚8 𝑛4 2 152. 14𝑎7 3𝑎 153. −10𝑦 3𝑦 − 8𝑦 𝑦 154. 8 3𝑥

155. IC

4?E

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

158. 09RUxS

�l

159. 8 6 160. 12 10 161. −48 2 162. −24𝑥0 33 163. −10 𝑥 26 164. 16 11 + 24 33 165. 30 + 20 7 166. −135 2 + 54 70 167. −18 + 7 3 168. 25 − 30 5 − 30 6 + 36 30 169. 15 + 15 5 − 12 6 − 12 30 170. 2 − 3 + 2 2 − 6 171. 154 + 20 6 172. 299 − 70 10 173. 4 2 − 3 6 + 4 3 − 9 174. −21 2 175. 42y 176. -‐90 177. 75 178. −25 𝑥 2 179. 12 − 2 15 180. 4 6 − 36 2 181. −10 𝑥 3𝑥 + 15𝑥 182. 10 3 − 5 5 − 2 6 + 10 183. 12 + 6 3 − 4 6 − 6 2 184. 4 5 − 4 3 − 8 30 + 24 2 185. 8 + 2 7


186. 3 + 2 − 3 3 − 6 187. 70 − 16 6 188. -‐11 189. (3m + 5)2 190. (3xy – 1)(9x2y2 + 3xy + 1)

191. /0dT

eT

192. -‐5a2

193. 70

194. 33

195. 74

196. 6

197. \8

198. 8 /90

199. 2 + 3

200. 63 f 7 38/

201. 63 f 8 0\

202. −8 − 4 3 − 2 5 − 15 203. −6 2 + 4 5 204. −6 − 2 6 + 3 5 + 30

205. /93

206. 2 3

207. \ 8/0

208. 3 /90

209. 0/7

210. −2 3

211. − /\− 8 0

/4

212. 4 76 8 0/8

213. −5 + 3 3

214. −1 − 74− 5 − 89

4

215. 0=f 4 /985

216. 3 363 86 /9f 708

217. 0de

218. 6x2 + 4x – 32 219. (3x – 1)(x + 4)

220. − 74e@

dl

221. -‐2 222. 4 223. -‐3x2 224. 5ab4 225. − /

?@

226. AU

DE

227. 1 228. -‐6 229. 3𝑥𝑦0 𝑥𝑦𝑧0S 230. 2𝑟0𝑠8𝑡8 4S 231. 15𝑚𝑛8𝑝0 6𝑚0𝑛S 232. 12𝑎0𝑏8𝑐4 𝑎0𝑏𝑐0S 233. -‐8 234. 7 235. -‐2x3 236. 9a2b7

237. − /kS

238. ml

nBB

239. 2 240. -‐5 241. 2𝑗𝑘 3𝑗𝑚S

242. 5𝑥0𝑦0𝑧0 5𝑦𝑧0S

243. 6𝑎0𝑏0𝑐 7𝑎𝑐0S 244. 12𝑥8𝑦𝑧3 5𝑦𝑧0S 245. 9 246. 8a3 – b3 247. 16x2 – 625y2 248. p = -‐28 249. Not a real number 250. -‐1 251. 5x4 252. 2 𝑥8 253. −𝑥0𝑦8𝑧4

254. ?S

4


255. uU uCU

v@

256. 2𝑛0 𝑚3𝑛3@ 257. 𝑥 27𝑥0𝑦8𝑧0C

258. 2 𝑥 𝑦𝑧0 3𝑦C

259. 8𝑥0𝑦8𝑧4 𝑥0𝑦𝑧0C

260. −𝑛4𝑝8 𝑚4𝑛4T 261. p – 3 262. (2x – 1)2 263. (r + 3p)3 264. 2x2y4

265. 8 /7U

0

266. − 𝑥0C 267. 2r

268. 0 FHGSU

G

269. ?HIU@

I

270. 0 03xHS

3

271. 0\kSC

8

272. 04?U

0?

273. Not a real number 274. -‐2 275. 2 𝑥3 276. 3x5 277. –x3yz2

278. ?C

7

279. kC kCU

yT

280. 2𝑎𝑏8 𝑎\𝑏E 281. 2𝑥0𝑦0𝑧0 7𝑥𝑦0𝑧8C

282. 63𝑥8𝑦3𝑧7 𝑥0𝑧0C 283. −6𝑎8𝑏= 𝑎8𝑏0@ 284. Cannot be simplified 285. (2r – 5)4 286. (2y – 1)2 287. 2𝑛𝑝0 𝑛T

288. 34?HIC

8?

289. 3 FHU

F

290. 74FG@T

0G

291. 87?S

8?

292. 039RSxSC

3R

293. 68 /7ICU

0I

294. 3 0?C

0

295. 8 048RU@

R

296. (12p – 1)(12p + 1) 297. 70 − 2 7 298. -‐27a9b-‐6

299. GH

/44FH

300. -‐2 301. 32 302. /

703

303. /=/

304. -‐2 305. 128

306. 4𝑚BH

307. 3𝑟BS𝑠

HS𝑡

CS

308. 3𝑥lC

309. 𝑥0S 310. 𝑎𝑏0𝑐8S 311. 4 𝑒7𝑓4𝑔5BH 312. 4x3 313. 243y3

314. /3703dBH

dH

315. eSH

3/0

316. /AC

317. 5𝑥BC

318. 𝑦CT

319. − �BBH

�

320. 125m6


321. -‐5 322. 8 323. /

80

324. -‐3 325. -‐2 326. /

=

327. 9𝑝UH

328. 𝑟CS𝑠𝑡

TS

329. 2𝑥SH

330. 𝑥S 331. 𝑎𝑏4𝑐7@ 332. 𝑚4𝑛39𝑝/3Hw 333. x2 334. y2

335. 4dHS

d

336. 0/=\e

337. AU@

A

338. 𝑥SC

339. 𝑦ST

340. FTBH

F

341. /=?l

342. 8ed

343. 9x2 – 4y2

344. /7dE

eB@

345. (1 – 2y)(1 + 2y + 4y2) 346. x = 32 347. a = 26 348. x = 8 349. t = -‐11 350. 𝑝 = 3

0

351. m = 2 352. x = 5 353. m = 2 354. No solution 355. x = 0

356. g = 48 357. x = 65 358. 𝑚 = =/

0

359. 𝑏 = − /30

360. 𝑥 = − 73

361. No real solution 362. x = 3 363. m = 2 364. t = 4 365. x = 1

366. d(D f /)eA

367. 8x2 – 10xy + 3y2 368. 3 10 − 3 6 369. =/

FEGBH

370. -‐60i 371. 384 372. -‐15i 373. 21 374. 8i 375. 54 376. i 377. 1 378. i 379. –i 380. i 381. -‐1 382. -‐20 383. −4 5 384. 3𝑖 5 385. −2𝑥= 14 386. −10 𝑝8 3 387. 4𝑖 3 388. 6ib2 389. 2𝑎𝑖 2 390. 4 𝑥8𝑦8 𝑖 2𝑦 391. 6𝑚0𝑛𝑖 2𝑛 392. 4𝑎 𝑏8 𝑖 3 393. 5x4y6i 394. 9i


395. -‐72 396. -‐6i 397. 20 398. -‐70i 399. 105 400. -‐1 401. –i 402. 1 403. 1 404. i 405. -‐1 406. –i 407. –i 408. -‐12 409. −6 15 410. 9i 411. −4 𝑚 412. −15𝑥4 15 413. 8i 414. 11b4i 415. 3𝑎8𝑖 2 416. 4𝑥0 𝑦8 𝑖 3𝑥 417. 4r6i 418. 2𝑥𝑖 3𝑥 419. 4𝑚8𝑛𝑖 6𝑚𝑛 420. 4 𝑎8𝑏\ 𝑖 2 421. 27p3 + q3 422. 12x7y2-‐ 4x3y 423. (4x + 3y)(16x2 – 12xy + 9y2) 424. I

?

425. 2 + 2i 426. -‐5 + i 427. -‐2 428. 8 + 2i 429. 9 + 6i 430. -‐6 – i 431. 20 – 10i 432. -‐2 – 12i 433. -‐4 – 12i 434. 24 – 18i 435. 9 + 38i

436. -‐6 – 22i 437. 7 + 11i 438. 10 439. -‐11 – 3i 440. 5 – 11i 441. 12 – 16i 442. 35 – 12i 443. -‐3 444. 10 + 3i 445. 10 + 5i 446. 0 447. 5 – 4i 448. -‐6 + i 449. 1 – 2i 450. 10 + 4i 451. -‐30 + 36i 452. 6 + 8i 453. 8 + 12i 454. -‐1 – i 455. 10 + 28i 456. 65 – 72i 457. 29 – 65i 458. -‐19 + 42i 459. 27 – 36i 460. 45 – 28i 461. 4q3 – 15q2 – 23q + 24 462. -‐6x2y – 2x2z 463. x3 – 9x2 + 27x – 27

464. ?DI(A f /)

465. -‐2i 466. − 8�

4

467. 0�8

468. 1 – 2i

469. 4�3

470. �0

471. \�3

472. − 80+ 2𝑖

473. 0 f 4�3


474. 65 f 8�/9

475. 5 f /5�07

476. 80 f 35�=3

477. -‐1 + i

478. 67 6 8�3

479. /6 �0

480. /4 f 3�/8

481. 6\6 �/9

482. /4 f =�/8

483. 5 6 /5�/8

484. 3 f 8�05

485. 3�8

486. − 0�3

487. 4�\

488. -‐1 – 4i 489. -‐3i 490. 4i 491. − 3�

\

492. 30− 3𝑖

493. /06 4�3

494. 60 f =�/\

495. / 6 =�/8

496. 08f//�03

497. 03 f /9�05

498. 64 f \�/3

499. 6/ 6 /\�05

500. 0/ f �07

501. 6/ f 8�3

502. / f 0�3

503. 0 f 5�3

504. 6/6/\�/9

505. (3m + 1)(2m – 7) 506. 9x2y2 – 1 507. 8x3 – y3

508. A(ef/)dD

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