NJCTL



Graphing Square Roots - Class WorkGraph the following equations by hand. State the domain and range of each using interval notation.31508701644652558691644651. y=-x+22. fx=-3x-1 31502351257302565401270003. y=-x+34. gx=-2x-1255905730253150779703035. y=-x+2+46. hx=-2x-4-331769051130302559051130307. y=3-x+28. y=4x-8-1Graphing Square Roots - HomeworkGraph the following equations by hand. State the domain and range of each using interval notation. 31985311754962197101746259. y=-x+210. fx=-12x319831312193821971015303511. y=-x-412. gx=-2x+3-1319849517335521971017335513. y=-12x+314. hx=3x+6-2319849516054621971015684515. y=4-2x+316. y=-3-3x-4Working with Square Roots - Class WorkSimplify each square root.17. 25 18. 64 19. -81 20. -81 21. 21254922. -1612123. 3614424. -122510025. -46426. 108127. -32528. 1629. 4-430. b2431. x432. y633. m1834. p1035. 144x636. c1436 37. 169d838. 49m1839. n24440. y1216Working with Square Roots - HomeworkSimplify each square root.41. 28942. -40043. 3644. 336145. -1000046. 2522547. 4919648. -128140049. -2366450. 5951. -319652. -74953. -1016954. a655. x856. m1057. t1258. x459. h21660. 4x16 61. 25d1262. 81y2263. g26964. r836Spiral Review65. Factor: 66. Multiply: 67. Simplify:68. Factor: 27m3 – 1 (x – 2y)(3x2 – 2xy + y) 25m3n75m7n5 2x2 – x + 5Irrational Roots - Class WorkPut in simplest radical form:69. 5070. -34871. 42072. 873. -27574. 10300c475. -12576. 72877. -56378. -87279. 121680. -21881. 324a682. -420x5y683. 1616m8n12 84. -2448r9s285. -632p2q10r486. 1006g3h1487. 564x10y688. -1330a7y289. -40xy240x24y1690. -3a3b96a9b391. 15m2n6120m4n6Irrational Roots - HomeworkPut in simplest radical form:92. 9693. -315094. 48095. -22496. -1250097. 4m2108m398. -512099. 3147100. 784101. -4320p9102. -820x6103. 4027104. -14n12105. 230r3s8 106. -88p4q10r5 107. -2016x20y2108. 775a5b15c6109. -10100g6h10110. -536j15k5111. 12a3b15112. -p3q580p13q25113. 9m4n372m7n8114. -4x5y4144x10y12Spiral 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 WorkSimplify each expression119. 1511 – 11120. 10 + 410121. 5 - 35122. 26 + 33123. 37 + 27124. -36 + 86125. 513 + 7313 - 413126. 53 - 2 - 33127. 27+3-348128. 48-212+432129. 245-720+380130. 212 - 727131. -424-354132. 4x27x4-x12x4133. 58y5+4y18y3134. 36m3n2-mmn2135. -2kp4+6p2k136. 32r5-48r5-312r5 Adding and Subtracting Radicals - HomeworkSimplify each expression137. 310+810138. 97-37139. 3+43140. 210-49-810141. 54+74+77142. 33+93+23143. 105-3-85144. 45 + 20145. 98 - 22146. 53 + 48147. 97 - 263148. 27 + 75149. -p3-pp 150. -4xx3-6x5151. 58m6n8+332m6n8152. 23a7+427a7153. -512y3-44y3154. 43x-63x+512xSpiral Review155. Simplify:156. Factor:157. Multiply:158. Simplify: 12x-2y-448x6y-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. (42)(23)160. (35)(42)161. (-26)(412)162. -83(3x211)163. (513x)(-22x)164. 811(2+33)165. 56(6+47) 166. -910(35-67)167. 4+533-23168. 5-655-66169. 3+355-46170. 2-31+2171. 2+562172. 7-5102173. 4-332+3Multiplying Radicals – HomeworkMultiply the following. Make sure answers are in simplest radical form.174. (-6)(73)175. (7y3)(23)176. (-33)(512)177. 5(3125)178. -510x(5x)179. -3(25-43)180. 43(2-36) 181. -5x(215x-3)182. 5-223-5183. 4+233-6184. 25-232-46185. 1+72186. 3+21-3187. 8-62188. 1-231+23Spiral Review189. Factor:190. Factor:191. Simplify:192. Simplify: 9m2 + 30m + 25 27x3y3 – 1 (3a3b-4)(4a4b-3) 125a3b-25abRationalizing the Denominator - Class WorkSimplify:193. 36194. 15195. 326196. 323197. 737198. 352199. 12-3200. 56+5201. 1-21+22202. 2+34-5203. 432+25204. 3+62+5Rationalizing the Denominator - HomeworkSimplify:205. 25206. 63207. 743208. 552209. 7367210. -262211. 12-32 212. 64+3 213. 3-33+23 214. 4+61-5215. 47-10216. 5-35+2Spiral Review217. Simplify:218. Multiply:219. Factor:220. Simplify: a3b6 (2x – 4)(3x + 8) 3x2 – 11x – 4 -4a-3b23Cube Roots - Class WorkSimplify:221. 3-8222. 364223. 3-27x6224. 3125a3b12225. 3-1x18226. 3c15d24227. 31228. 3-216229. 327x4y7z2230. 332r6s9t9231. 5mn2 354m2n4p6232. 3ab 364a5b7c14Cube Roots - HomeworkSimplify:233. 3-512234. 3343235. 3-8x9236. 3729a6b21237. 3-1p9238. 3j27k33239. 38240. 3-125241. 324j4k3m242. 3625x6y7z8243. 3ab356a4b3c5244. 6x2z4 340x3y4z5Spiral Review245. Simplify: 246. Multiply:247. Multiply: 248. Solve: 3x33x-3 (2a – b)(4a2 + 2ab + b2) (4x – 25y)(4x + 25y) 2(p – 5) – 3(p + 1) = 15nth roots - Class WorkSimplify:249. 4-81250. 5-1251. 4625x16252. 664x18253. 5-x10y15z20254. 4x12256255. 5e29f30256. 664m5n17257. 427x6y3z2258. 448x4y5z8259. 4x 416x6y13z18260. 7-m4n32p21261. 5p-35262. 32x-16263. 6r+3p18264. 416x8y16265. 352266. -x4x2267. 132r2268. 25m25n2269. 6x2y270. 2t35t271. 4p33272. 534x4nth roots - HomeworkSimplify:273. 4-16274. 5-32275. 416x20276. 6729x30277. 5-x15y5z10278. 4x161296279. 5p24q35280. 8256a15b25281. 4112x9y10z11282. 7x3y4z5 481x2y4z6283. -3ab3664a15b32284. 6m+23285. 32r-512286. 52y-110287. 7128n8p14288. 42y3x2 289. 45m3290. 7m2n291. 3433x2292. 42t35r293. -352y294. 5x48x3295. 963rSpiral Review296. Factor:297. Multiply:298. Simplify:299. Simplify: 144p2 – 1 710-2 -3a3b-23 12mn-2Rational Exponents - Class WorkSimplify: 300. -3215 301. 452302. 125-43303. 27-43304. -18-13305. 1674Write each expression without the radical.306. 16m307. 327rs2t4308. 481x9Write each expression using a single radical.309. x23310. a13b23c311. e12f13g34Simplify. Leave answers with positive exponents. 312. 4x612313. 27y6553314. 25a-1262315. 16b-23-94316. c-2510317. 5xx34318. yy37319. -z14z12z23320. 25m432Rational Exponents – HomeworkSimplify: 321. -12513322. 432323. 16-54324. -2713325. -132-15326. 4-32Write each expression without the radical.327. 81p5328. 3r4s3t7329. 416x6Write each expression using a single radical.330. x13331. a16b23c332. m15n52p34Simplify. Leave answers with positive exponents. 333. x412334. y4552335. 4a-13336. 9b-27144337. c-3849338. xx14339. yy47340. m16m14m13341. 16x12-34Spiral Review342. Simplify:343. Multiply: 344. Simplify:345. Factor: 3aba2b2 (3x + 4y)(3x – 4y) 2a2b-44 1 – 8y3Solving Radical Equations - Class WorkSolve each of the following equations.346. 32x=24347. 3a+1=3348. 42x=2349. 10=23-2t350. 3-2p-413=2351. m+2=2m352. 34x+1-36x-9=0353. 812=4m12354. t+1=t-1355. 2x+4=2x+2Solving Radical Equations - HomeworkSolve each of the following equations.356. 3g=12357. 3x-1=4358. 42m=3359. 12=26-4b360. 4-35x-213=10361. 4y+5=2y-6362. 35x+2-38x-7=0363. 613=3m13364. -t+4-t=-2365. x+3=x+1Spiral Review366. Simplify:367. Multiply:368. Multiply:369. Simplify: abcd + 1 (2x – y)(4x – 3y) 325-3 -3m-2n-34Complex Numbers - Class WorkSimplify using i.370. 3i?4i?5i371. -2i?4i?-6i?8i372. -i?5i?-3i373. i?-3i?7i?-i374. 2i?2i?-2i375. -6i?3i?-3i?i376. i9377. -i22378. i73379. -i25380. i33 381. i46382. -16?-25383. -8?-10384. -45385. -4x9?-14x7386. -30p4?-10p2387. -48388. -36b4389. -8a2390. -32x6y7391. -72m4n3392. -48a2b6393. -25x8y12Complex Numbers - HomeworkSimplify using i.394. -i?3i?3i395. -4i?2i?-9i?-i396. 3i?i?2i397. i?4i?-i?-5i398. 2i?5i?7i399. -i?-3i?-5i?-7i400. i10401. i23402. i72403. -i42404. -i15405. i66406. i19407. -i93408. -9?-4409. -12?-75410. -81411. -4m?-4m412. -27x6?-125x2413. -64414. -121b8415. -18a6416. -48x5y6417. -16r12418. -24x3419. -96m7n3420. -32a6b14Spiral Review421. Multiply:422. Multiply:423. Factor:424. Simplify:(3p + q)(9p2 – 3pq + q2) 4x3y(3x4y – 1) 64x3 + 27y3 xyx2y2Adding, Subtracting, and Multiplying Complex Numbers - Class WorkSimplify:425. 6+5i-4+3i426. -3+2i+-2-i427. 3-i-5-i428. 3+5i+5-3i429. 7+4i--2-2i430. -3-2i-3-i431. 54-2i432. 2i-6+i433. -4i3-i434. -6-4+3i435. 6+5i4+3i436. 7+4i-2-2i437. -2+9i1-i438. 3-i3+i439. -3-2i3-i440. 8-3i1-i441. 4-2i2442. (-6+i)2Adding, Subtracting, and Multiplying Complex Numbers - HomeworkSimplify:443. -1+i+-2-i444. 7-2i--3-5i445. 2+3i+8+2i446. 4+9i+-4-9i447. 10-7i-5-3i448. 2+3i-8+2i449. -2-i--3+i450. 7+2i+3+2i451. -65-6i452. 2i4-3i453. -4i-3+2i454. -i1-i455. 2+3i8+2i456. 4+9i-4-9i457. 10-7i5-3i458. -6-i2-7i459. 6-3i2460. (-7+2i)2Spiral Review461. Multiply:462. Multiply:463. Work out:464. Simplify:(4q – 3)(q2 – 3q – 8) -2x2(3y + z) (x – 3)3 xc+1ydDividing Complex Numbers - Class WorkSimplify465. 2i 466. 34i467. -23i468. 2+ii469. -45i470. -12i471. -75i472. -4-3i2i473. 21-2i474. 3i1-3i475. 1 +4i5 + i476. 7-2i2-9i477. 2i1 - i478. -32 - i479. 2 - i3 + i480. 4 - i3 - 2i481. -2 - i3 + i482. 107 - 4i483. 5 - 3i3 + 2i484. 9 - 3i5 - 2iDividing Complex Numbers - HomeworkSimplify485. -53i486. 25i487. -47i488. 4-ii489. 3i490. -4i491. 57i492. 6 +5 i2i493. 83 + i494. 2i4 - i495. 2 - i2 + 3i496. 5 - i4 - 3i497. 55 - 2i498. -3 + 2i6 + 3i499. 1 - 3i5 + 2i500. 1 - 4i1 - 5i501. 2i3 - i502. 2 + i4 - 3i503. -1 + 4i2 + i504. 5 - 2i1 + 3iSpiral Review505. Factor:506. Multiply:507. Multiply:508. Simplify: 6m2 – 19m – 7(3xy – 1)(3xy + 1)(2x – y)(4x2 + 2xy + y2) cdab + 1Radicals Answer Key2717071019281. 465038956672. 3810001917703. 27150731754. 271707151135. 6. 1670051270 2599521280527. 25964312708. 3009901892309. 2593529044310.53086012636511. 36893515811512. 307957-14107913. 39116016573514. 52236663515. 5219706096016. 58-9Not a real number15Not a real number126-3290-154Not a real numberb12x2y3m9p512x3c7613d47m9n122y6417-20657-1001312-275-215-42-49-130a3x4m6t6x2h42x85d69y11g133r46(3m – 1)(9m2 + 3m + 1)3x3 – 8x2y + xy + 4xy2 – 2y25n2m4(x + 3)(2x – 5)52-1238522-103100c23Not a real number147-157-48248-626a36-8x2y35x64m4n6-96r4s3r-24pq5r22100gh76g40x5y3-13a3y30a-80x13y1010-12a7b26ab30m4n946-156165-46-120524m33m-1030213 1421 -32p45p -16x35 1203 –n614 2rs430 -16p2q5r22r -80x10y 35a2b7c33ab -100g3h5 -30j14k2jk 12ab7ab -4p9q175pq 54m7n72m -48x5x5y10 x=38 5x-4y5x+4y 20m9n3 3p(4p – 1) 1411 510 -25 26+33 57 56 13+7313 23-2 -83 242-43 45 -173 -176 10x33 22y22y 5mnm 4p2k -5r22r-6r23r 1110 67 53 -12-610 24+77 143 25-3 65 52 93 37 83 -2pp -10x2x 22m3n42 14a63a -10y3y-8yy 83x y44x8 (4p + 5q)(16p2 – 20pq + 25p2) 6a2 – a – 35 20r5t3s9 86 1210 -482 -24x233 -10x26 1611+2433 30+207 -1352+5470 -18+73 25-305-306+3630 15+155-126-1230 2-3+22-6 154+206 299-7010 42-36+43-9 -212 42y -90 75 -25x2 12-215 46-362 -10x3x+15x 103-55-26+10 12+63-46-62 45-43-830+242 8+27 3+2-33-6 70-166 -11 (3m + 5)2 (3xy – 1)(9x2y2 + 3xy + 1) 12a7b7 -5a2 62 55 64 6 73 3102 2+3 -5 + 6531 -5 + 327 -8-43-25-15 -62+45 -6-26+35+30 105 23 7312 5102 216 -23 -17-3214 46- 3213 -5+33 -1-64-5-304 28+ 41039 55-53-10+623 2ab 6x2 + 4x – 32 (3x – 1)(x + 4) -64b6a9 -2 4 -3x2 5ab4 -1x6 c5d8 1 -6 3xy23xyz2 2r2s3t334 15mn3p236m2n 12a2b3c43a2bc2 -8 7 -2x3 9a2b7 -1p3 j9k11 2 -5 2jk33jm 5x2y2z235yz2 6a2b2c37ac2 12x3yz535yz2 9 8a3 – b3 16x2 – 625y2 p = -28 Not a real number -1 5x4 2x3 -x2y3z4 x34 e55e4f6 2n26m5n5 x427x2y3z2 2xyz243y 8x2y3z44x2yz2 -n4p37m4n4 p – 3 (2x – 1)2 (r + 3p)3 2x2y4 35162 -4x2 2r 25m2n3n 6x2y5y 2325t25 427p33 524x2x Not a real number -2 2x5 3x5 –x3yz2 x46 p45p4q7 2ab38a7b 2x2y2z247xy2z3 63x3y5z64x2z2 -6a3b86a3b2 Cannot be simplified (2r – 5)4 (2y – 1)2 2np27n 454x2y3x 55m2m 764mn62n 336x3x 4250r3t35r -3516y42y 542x2 36243r5r (12p – 1)(12p + 1) 70-27 -27a9b-6 n2144m2 -2 32 1625 181 -2 128 4m12 3r13s23t43 3x94 3x2 3ab2c3 412e6f4g9 4x3 243y3 15625a12a2 b32512 1c4 5x14 y47 -z112z 125m6 -5 8 132 -3 -2 18 9p52 r43st73 2x32 3x 6ab4c6 20m4n50p15 x2 y2 4a23a 2187b c56c x34 y37 m712m 18x9 3ba 9x2 – 4y2 16a8b16 (1 – 2y)(1 + 2y + 4y2) x = 32 a = 26 x = 8 t = -11 p=52 m = 2 x = 5 m = 2 No solution x = 0 g = 48 x = 65 m=812 b=-152 x=-65 No real solution x = 3 m = 2 t = 4 x = 1 a(d + 1)bc 8x2 – 10xy + 3y2 310-36 81m8n12 -60i 384 -15i 21 8i 54 i 1 i –i i -1 -20 -45 3i5 -2x814 -10p33 4i3 6ib2 2ai2 4x3y3i2y 6m2ni2n 4ab3i3 5x4y6i 9i -72 -6i 20 -70i 105 -1 –i 1 1 i -1 –i –i -12 -615 9i -4m -15x415 8i 11b4i 3a3i2 4x2y3i3x 4r6i 2xi3x 4m3ni6mn 4a3b7i2 27p3 + q3 12x7y2- 4x3y (4x + 3y)(16x2 – 12xy + 9y2) yx 2 + 2i -5 + i -2 8 + 2i 9 + 6i -6 – i 20 – 10i -2 – 12i -4 – 12i 24 – 18i 9 + 38i -6 – 22i 7 + 11i 10 -11 – 3i 5 – 11i 12 – 16i 35 – 12i -3 10 + 3i 10 + 5i 0 5 – 4i -6 + i 1 – 2i 10 + 4i -30 + 36i 6 + 8i 8 + 12i -1 – i 10 + 28i 65 – 72i 29 – 65i -19 + 42i 27 – 36i 45 – 28i 4q3 – 15q2 – 23q + 24 -6x2y – 2x2z x3 – 9x2 + 27x – 27 xdy(c + 1) -2i -3i4 2i3 1 – 2i 4i5 i2 7i5 -32+2i 2 + 4i5 -9 + 3i10 9 + 19i26 32 + 59i85 -1 + i -6 - 3i5 1- i2 14 + 5i13 -7- i10 14 + 8i13 9 - 19i13 5 + 3i29 5i3 -2i5 4i7 -1 – 4i -3i 4i -5i7 52-3i 12- 4i5 -2 + 8i17 1 - 8i13 23+11i25 25 + 10i29 -4 + 7i15 -1 - 17i29 21 + i26 -1 + 3i5 1 + 2i5 2 + 9i5 -1-17i10 (3m + 1)(2m – 7) 9x2y2 – 1 8x3 – y3 c(b+1)ad ................
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