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328开平方等于多少

发布时间: 2022-04-19 00:18:52

A. 求平方根与立方根表

呵呵
方根:
√0 = 0(表示根号0等于0,下同)
√1 = 1
√2 = 1.4142135623731
√3 = 1.73205080756888
√4 = 2
√5 = 2.23606797749979
√6 = 2.44948974278318
√7 = 2.64575131106459
√8 = 2.82842712474619
√9 = 3
√10 = 3.16227766016838
√11 = 3.3166247903554
√12 = 3.46410161513775
√13 = 3.60555127546399
√14 = 3.74165738677394
√15 = 3.87298334620742
√16 = 4
√17 = 4.12310562561766
√18 = 4.24264068711928
√19 = 4.35889894354067
√20 = 4.47213595499958
√21 = 4.58257569495584
√22 = 4.69041575982343
√23 = 4.79583152331272
√24 = 4.89897948556636
√25 = 5
√26 = 5.09901951359278
√27 = 5.19615242270663
√28 = 5.29150262212918
√29 = 5.3851648071345
√30 = 5.47722557505166
√31 = 5.56776436283002
√32 = 5.65685424949238
√33 = 5.74456264653803
√34 = 5.8309518948453
√35 = 5.91607978309962
√36 = 6
√37 = 6.08276253029822
√38 = 6.16441400296898
√39 = 6.2449979983984
√40 = 6.32455532033676
√41 = 6.40312423743285
√42 = 6.48074069840786
√43 = 6.557438524302
√44 = 6.6332495807108
√45 = 6.70820393249937
√46 = 6.78232998312527
√47 = 6.85565460040104
√48 = 6.92820323027551
√49 = 7
√50 = 7.07106781186548
√51 = 7.14142842854285
√52 = 7.21110255092798
√53 = 7.28010988928052
√54 = 7.34846922834953
√55 = 7.41619848709566
√56 = 7.48331477354788
√57 = 7.54983443527075
√58 = 7.61577310586391
√59 = 7.68114574786861
√60 = 7.74596669241483
√61 = 7.81024967590665
√62 = 7.87400787401181
√63 = 7.93725393319377
√64 = 8
√65 = 8.06225774829855
√66 = 8.12403840463596
√67 = 8.18535277187245
√68 = 8.24621125123532
√69 = 8.30662386291807
√70 = 8.36660026534076
√71 = 8.42614977317636
√72 = 8.48528137423857
√73 = 8.54400374531753
√74 = 8.60232526704263
√75 = 8.66025403784439
√76 = 8.71779788708135
√77 = 8.77496438739212
√78 = 8.83176086632785
√79 = 8.88819441731559
√80 = 8.94427190999916
√81 = 9
√82 = 9.05538513813742
√83 = 9.1104335791443
√84 = 9.16515138991168
√85 = 9.21954445729289
√86 = 9.2736184954957
√87 = 9.32737905308882
√88 = 9.38083151964686
√89 = 9.4339811320566
√90 = 9.48683298050514
√91 = 9.53939201416946
√92 = 9.59166304662544
√93 = 9.64365076099295
√94 = 9.69535971483266
√95 = 9.74679434480896
√96 = 9.79795897113271
√97 = 9.8488578017961
√98 = 9.89949493661167
√99 = 9.9498743710662
√100 = 10
√101 = 10.0498756211209
√102 = 10.0995049383621
√103 = 10.1488915650922
√104 = 10.1980390271856
√105 = 10.2469507659596
√106 = 10.295630140987
√107 = 10.3440804327886
√108 = 10.3923048454133
√109 = 10.4403065089106
√110 = 10.4880884817015
√111 = 10.5356537528527
√112 = 10.5830052442584
√113 = 10.6301458127347
√114 = 10.6770782520313
√115 = 10.7238052947636
√116 = 10.770329614269
√117 = 10.816653826392
√118 = 10.8627804912002
√119 = 10.9087121146357
√120 = 10.9544511501033
√121 = 11
√122 = 11.0453610171873
√123 = 11.0905365064094
√124 = 11.13552872566
√125 = 11.1803398874989
√126 = 11.2249721603218
√127 = 11.2694276695846
√128 = 11.3137084989848
√129 = 11.3578166916005
√130 = 11.4017542509914
√131 = 11.4455231422596
√132 = 11.4891252930761
√133 = 11.5325625946708
√134 = 11.5758369027902
√135 = 11.6189500386223
√136 = 11.6619037896906
√137 = 11.7046999107196
√138 = 11.7473401244707
√139 = 11.7898261225516
√140 = 11.8321595661992
√141 = 11.8743420870379
√142 = 11.916375287813
√143 = 11.9582607431014
√144 = 12
√145 = 12.0415945787923
√146 = 12.0830459735946
√147 = 12.1243556529821
√148 = 12.1655250605964
√149 = 12.2065556157337
√150 = 12.2474487139159
√151 = 12.2882057274445
√152 = 12.328828005938
√153 = 12.369316876853
√154 = 12.4096736459909
√155 = 12.4498995979887
√156 = 12.4899959967968
√157 = 12.5299640861417
√158 = 12.5698050899765
√159 = 12.6095202129185
√160 = 12.6491106406735
√161 = 12.6885775404495
√162 = 12.7279220613579
√163 = 12.7671453348037
√164 = 12.8062484748657
√165 = 12.8452325786651
√166 = 12.8840987267251
√167 = 12.9228479833201
√168 = 12.9614813968157
√169 = 13
√170 = 13.0384048104053
√171 = 13.076696830622
√172 = 13.114877048604
√173 = 13.1529464379659
√174 = 13.1909059582729
√175 = 13.228756555323
√176 = 13.2664991614216
√177 = 13.3041346956501
√178 = 13.3416640641263
√179 = 13.3790881602597
√180 = 13.4164078649987
√181 = 13.4536240470737
√182 = 13.490737563232
√183 = 13.5277492584687
√184 = 13.5646599662505
√185 = 13.6014705087354
√186 = 13.6381816969859
√187 = 13.6747943311773
√188 = 13.7113092008021
√189 = 13.7477270848675
√190 = 13.7840487520902
√191 = 13.8202749610853
√192 = 13.856406460551
√193 = 13.8924439894498
√194 = 13.9283882771841
√195 = 13.9642400437689
√196 = 14
√197 = 14.0356688476182
√198 = 14.0712472794703
√199 = 14.1067359796659
√200 = 14.142135623731
√201 = 14.1774468787578
√202 = 14.2126704035519
√203 = 14.247806848775
√204 = 14.2828568570857
√205 = 14.3178210632764
√206 = 14.3527000944073
√207 = 14.3874945699382
√208 = 14.422205101856
√209 = 14.456832294801
√210 = 14.4913767461894
√211 = 14.5258390463339
√212 = 14.560219778561
√213 = 14.5945195193264
√214 = 14.6287388383278
√215 = 14.6628782986152
√216 = 14.6969384566991
√217 = 14.7309198626562
√218 = 14.7648230602334
√219 = 14.7986485869487
√220 = 14.8323969741913
√221 = 14.8660687473185
√222 = 14.8996644257513
√223 = 14.9331845230681
√224 = 14.9666295470958
√225 = 15
√226 = 15.0332963783729
√227 = 15.0665191733194
√228 = 15.0996688705415
√229 = 15.1327459504216
√230 = 15.1657508881031
√231 = 15.1986841535707
√232 = 15.2315462117278
√233 = 15.2643375224737
√234 = 15.2970585407784
√235 = 15.3297097167559
√236 = 15.3622914957372
√237 = 15.3948043183407
√238 = 15.4272486205415
√239 = 15.4596248337403
√240 = 15.4919333848297
√241 = 15.52417469626
√242 = 15.556349186104
√243 = 15.5884572681199
√244 = 15.6204993518133
√245 = 15.6524758424985
√246 = 15.6843871413581
√247 = 15.7162336455017
√248 = 15.7480157480236
√249 = 15.7797338380595
√250 = 15.8113883008419
√251 = 15.8429795177549
√252 = 15.8745078663875
√253 = 15.9059737205869
√254 = 15.9373774505092
√255 = 15.9687194226713
√256 = 16
√257 = 16.0312195418814
√258 = 16.062378404209
√259 = 16.0934769394311
√260 = 16.1245154965971
√261 = 16.1554944214035
√262 = 16.1864140562386
√263 = 16.2172747402269
√264 = 16.2480768092719
√265 = 16.2788205960997
√266 = 16.3095064303001
√267 = 16.3401346383682
√268 = 16.3707055437449
√269 = 16.4012194668567
√270 = 16.431676725155
√271 = 16.4620776331543
√272 = 16.4924225024706
√273 = 16.5227116418583
√274 = 16.5529453572468
√275 = 16.583123951777
√276 = 16.6132477258362
√277 = 16.6433169770932
√278 = 16.6733320005331
√279 = 16.7032930884901
√280 = 16.7332005306815
√281 = 16.7630546142402
√282 = 16.7928556237467
√283 = 16.8226038412607
√284 = 16.8522995463527
√285 = 16.8819430161341
√286 = 16.9115345252878
√287 = 16.9410743460974
√288 = 16.9705627484771
√289 = 17
√290 = 17.0293863659264
√291 = 17.058722109232
√292 = 17.0880074906351
√293 = 17.1172427686237
√294 = 17.1464281994822
√295 = 17.1755640373177
√296 = 17.2046505340853
√297 = 17.2336879396141
√298 = 17.2626765016321
√299 = 17.2916164657906
√300 = 17.3205080756888
√301 = 17.3493515728975
√302 = 17.3781471969828
√303 = 17.4068951855292
√304 = 17.4355957741627
√305 = 17.464249196573
√306 = 17.4928556845359
√307 = 17.5214154679352
√308 = 17.5499287747842
√309 = 17.5783958312469
√310 = 17.606816861659
√311 = 17.6351920885484
√312 = 17.6635217326557
√313 = 17.6918060129541
√314 = 17.7200451466693
√315 = 17.7482393492988
√316 = 17.7763888346312
√317 = 17.8044938147649
√318 = 17.832554500127
√319 = 17.8605710994918
√320 = 17.8885438199983
√321 = 17.9164728671689
√322 = 17.9443584449264
√323 = 17.9722007556114
√324 = 18
√325 = 18.0277563773199
√326 = 18.0554700852678
√327 = 18.0831413200251
√328 = 18.1107702762748
√329 = 18.1383571472171
√330 = 18.1659021245849
√331 = 18.1934053986603
√332 = 18.2208671582886
√333 = 18.2482875908947
√334 = 18.2756668824971
√335 = 18.3030052177231
√336 = 18.3303027798234
√337 = 18.3575597506858
√338 = 18.3847763108502
√339 = 18.411952639522
√340 = 18.4390889145858
√341 = 18.4661853126194
√342 = 18.4932420089069
√343 = 18.5202591774521
√344 = 18.5472369909914
√345 = 18.5741756210067
√346 = 18.6010752377383
√347 = 18.6279360101972
√348 = 18.6547581061776
√349 = 18.6815416922694
√350 = 18.7082869338697
√351 = 18.7349939951952
√352 = 18.7616630392937
√353 = 18.7882942280559
√354 = 18.8148877222268
√355 = 18.8414436814168
√356 = 18.8679622641132
√357 = 18.8944436276912
√358 = 18.9208879284245
√359 = 18.9472953214964
√360 = 18.9736659610103
√361 = 19
√362 = 19.0262975904404
√363 = 19.0525588832577
√364 = 19.0787840283389
√365 = 19.1049731745428
√366 = 19.131126469709
√367 = 19.157244060668
√368 = 19.1833260932509
√369 = 19.2093727122985
√370 = 19.2353840616713
√371 = 19.2613602842582
√372 = 19.2873015219859
√373 = 19.313207915828
√374 = 19.3390796058137
√375 = 19.3649167310371
√376 = 19.3907194296653
√377 = 19.4164878389476
√378 = 19.4422220952236
√379 = 19.4679223339318
√380 = 19.4935886896179
√381 = 19.5192212959431
√382 = 19.5448202856921
√383 = 19.5703857907809
√384 = 19.5959179422654
√385 = 19.6214168703486
√386 = 19.6468827043885
√387 = 19.672315572906
√388 = 19.6977156035922
√389 = 19.723082923316
√390 = 19.7484176581315
√391 = 19.7737199332852
√392 = 19.7989898732233
√393 = 19.824227601599
√394 = 19.8494332412792
√395 = 19.8746069143518
√396 = 19.8997487421324
√397 = 19.9248588451713
√398 = 19.94993734326
√399 = 19.9749843554382
√400 = 20
√401 = 20.0249843945008
√402 = 20.0499376557634
√403 = 20.0748598998847
√404 = 20.0997512422418
√405 = 20.1246117974981
√406 = 20.1494416796099
√407 = 20.174241001832
√408 = 20.1990098767242
√409 = 20.2237484161567
√410 = 20.2484567313166
√411 = 20.2731349327133
√412 = 20.2977831301844
√413 = 20.3224014329016
√414 = 20.3469899493758
√415 = 20.3715487874634
√416 = 20.3960780543711
√417 = 20.4205778566621
√418 = 20.4450483002609
√419 = 20.4694894904587
√420 = 20.4939015319192
√421 = 20.5182845286832
√422 = 20.5426385841741
√423 = 20.5669638012031
√424 = 20.591260281974
√425 = 20.6155281280883
√426 = 20.6397674405503
√427 = 20.6639783197718
√428 = 20.6881608655772
√429 = 20.712315177208
√430 = 20.7364413533277
√431 = 20.7605394920267
√432 = 20.7846096908265
√433 = 20.8086520466848
√434 = 20.8326666559997
√435 = 20.8566536146142
√436 = 20.8806130178211
√437 = 20.9045449603669
√438 = 20.9284495364563
√439 = 20.952326839757
√440 = 20.976176963403
√441 = 21
√442 = 21.0237960416286
√443 = 21.0475651798492
√444 = 21.0713075057055
√445 = 21.095023109729
√446 = 21.1187120819429
√447 = 21.142374511866
√448 = 21.1660104885167
√449 = 21.1896201004171
√450 = 21.2132034355964
√451 = 21.2367605815953
√452 = 21.2602916254693
√453 = 21.2837966537928
√454 = 21.3072757526625
√455 = 21.3307290077015
√456 = 21.3541565040626
√457 = 21.3775583264319
√458 = 21.4009345590327
√459 = 21.4242852856286
√460 = 21.4476105895272
√461 = 21.4709105535839
√462 = 21.4941852602047
√463 = 21.51743479135
√464 = 21.540659228538
√465 = 21.5638586528478
√466 = 21.5870331449229
√467 = 21.6101827849743
√468 = 21.6333076527839
√469 = 21.6564078277077
√470 = 21.6794833886788
√471 = 21.7025344142107
√472 = 21.7255609824004
√473 = 21.7485631709315
√474 = 21.7715410570772
√475 = 21.7944947177034
√476 = 21.8174242292714
√477 = 21.8403296678416
√478 = 21.8632111090754
√479 = 21.8860686282393
√480 = 21.9089023002066
√481 = 21.9317121994613
√482 = 21.9544984001002
√483 = 21.9772609758359
√484 = 22
√485 = 22.0227155455452
√486 = 22.0454076850486
√487 = 22.0680764907139
√488 = 22.0907220343745
√489 = 22.113344387496
√490 = 22.1359436211787
√491 = 22.1585198061603
√492 = 22.1810730128188
√493 = 22.2036033111745
√494 = 22.2261107708929
√495 = 22.248595461287
√496 = 22.2710574513201
√497 = 22.293496809608
√498 = 22.3159136044214
√499 = 22.3383079036887
√500 = 22.3606797749979

立方根
3√0 = 0
3√1 = 1
3√2 = 1.25992104989487
3√3 = 1.44224957030741
3√4 = 1.5874010519682
3√5 = 1.7099759466767
3√6 = 1.81712059283214
3√7 = 1.91293118277239
3√8 = 2
3√9 = 2.0800838230519
3√10 = 2.15443469003188
3√11 = 2.22398009056932
3√12 = 2.28942848510666
3√13 = 2.35133468772076
3√14 = 2.41014226417523
3√15 = 2.46621207433047
3√16 = 2.51984209978975
3√17 = 2.57128159065824
3√18 = 2.6207413942089
3√19 = 2.66840164872194
3√20 = 2.71441761659491
3√21 = 2.75892417638112
3√22 = 2.80203933065539
3√23 = 2.84386697985157
3√24 = 2.88449914061482
3√25 = 2.92401773821287
3√26 = 2.96249606840737
3√27 = 3
3√28 = 3.03658897187566
3√29 = 3.07231682568585
3√30 = 3.10723250595386
3√31 = 3.14138065239139
3√32 = 3.1748021039364
3√33 = 3.20753432999583
3√34 = 3.23961180127748
3√35 = 3.27106631018859
3√36 = 3.30192724889463
3√37 = 3.33222185164595
3√38 = 3.36197540679896
3√39 = 3.39121144301417
3√40 = 3.41995189335339
3√41 = 3.44821724038273
3√42 = 3.47602664488645
3√43 = 3.50339806038672
3√44 = 3.53034833532606
3√45 = 3.55689330449006
3√46 = 3.58304787101595
3√47 = 3.60882608013869
3√48 = 3.63424118566428
3√49 = 3.65930571002297
3√50 = 3.68403149864039
3√51 = 3.70842976926619
3√52 = 3.73251115681725
3√53 = 3.75628575422107
3√54 = 3.77976314968462
3√55 = 3.80295246076139
3√56 = 3.82586236554478
3√57 = 3.8485011312768
3√58 = 3.8708766406278
3√59 = 3.89299641587326
3√60 = 3.91486764116886
3√61 = 3.93649718310217
3√62 = 3.95789160968041
3√63 = 3.97905720789639
3√64 = 4
3√65 = 4.02072575858906
3√66 = 4.04124002062219
3√67 = 4.06154810044568
3√68 = 4.08165510191735
3√69 = 4.10156592970235
3√70 = 4.12128529980856
3√71 = 4.14081774942285
3√72 = 4.16016764610381
3√73 = 4.17933919638123
3√74 = 4.19833645380841
3√75 = 4.21716332650875
3√76 = 4.23582358425489
3√77 = 4.25432086511501
3√78 = 4.27265868169792
3√79 = 4.29084042702621
3√80 = 4.30886938006377
3√81 = 4.32674871092222
3√82 = 4.34448148576861
3√83 = 4.36207067145484
3√84 = 4.37951913988789
3√85 = 4.39682967215818
3√86 = 4.4140049624421
3√87 = 4.43104762169363
3√88 = 4.44796018113863
3√89 = 4.46474509558454
3√90 = 4.48140474655716
3√91 = 4.49794144527541
3√92 = 4.514357435474
3√93 = 4.53065489608349
3√94 = 4.54683594377634
3√95 = 4.56290263538697
3√96 = 4.57885697021333
3√97 = 4.59470089220704
3√98 = 4.61043629205845
3√99 = 4.62606500918274
3√100 = 4.64158883361278
3√101 = 4.65700950780383
3√102 = 4.67232872835526
3√103 = 4.6875481476536
3√104 = 4.70266937544151
3√105 = 4.7176939803
3√106 = 4.73262349116337
3√107 = 4.7474593985234
3√108 = 4.7622031559046
3√109 = 4.77685618103502
3√110 = 4.79141985706278
3√111 = 4.80589553370533
3√112 = 4.82028452835046
3√113 = 4.83458812711164
3√114 = 4.84880758583988
3√115 = 4.86294413109428
3√116 = 4.87699896107331
3√117 = 4.89097324650875
3√118 = 4.90486813152402
3√119 = 4.91868473445873
3√120 = 4.93242414866094
3√121 = 4.9460874432487
3√122 = 4.9596756638423
3√123 = 4.97318983326859
3√124 = 4.98663095223865
3√125 = 5
3√126 = 5.01329793496458
3√127 = 5.02652569531348
3√128 = 5.03968419957949
3√129 = 5.05277434720856
3√130 = 5.06579701910089
3√131 = 5.0787530781327
3√132 = 5.09164336965949
3√133 = 5.10446872200146
3√134 = 5.11722994691205
3√135 = 5.12992784003009
3√136 = 5.14256318131647
3√137 = 5.15513673547577
3√138 = 5.16764925236362
3√139 = 5.18010146738029
3√140 = 5.1924941018511
3√141 = 5.2048278633942
3√142 = 5.21710344627617
3√143 = 5.22932153175598
3√144 = 5.24148278841779
3√145 = 5.2535878724929
3√146 = 5.26563742817144
3√147 = 5.27763208790408
3√148 = 5.28957247269421
3√149 = 5.3014591923809
3√150 = 5.31329284591305
3√151 = 5.32507402161499
3√152 = 5.33680329744389
3√153 = 5.34848124123936
3√154 = 5.36010841096536
3√155 = 5.37168535494483
3√156 = 5.38321261208728
3√157 = 5.39469071210959
3√158 = 5.40612017575022
3√159 = 5.41750151497718
3√160 = 5.42883523318981
3√161 = 5.4401218254148
3√162 = 5.45136177849642
3√163 = 5.4625555712814
3√164 = 5.47370367479843
3√165 = 5.48480655243262
3√166 = 5.49586466009501
3√167 = 5.50687844638735
3√168 = 5.51784835276224
3√169 = 5.52877481367887
3√170 = 5.53965825675446
3√171 = 5.55049910291155
3√172 = 5.56129776652124
3√173 = 5.57205465554262
3√174 = 5.58277017165842
3√175 = 5.59344471040698
3√176 = 5.60407866131077
3√177 = 5.61467240800149
3√178 = 5.62522632834186
3√179 = 5.63574079454424
3√180 = 5.64621617328617
3√181 = 5.65665282582291
3√182 = 5.66705110809706
3√183 = 5.67741137084543
3√184 = 5.68773395970313
3√185 = 5.69801921530506
3√186 = 5.70826747338486
3√187 = 5.71847906487132
3√188 = 5.72865431598244
3√189 = 5.73879354831717
3√190 = 5.74889707894483
3√191 = 5.7589652204924
3√192 = 5.76899828122963
3√193 = 5.77899656515213
3√194 = 5.7889603720624
3√195 = 5.798889997649
3√196 = 5.8087857335637
3√197 = 5.81864786749696
3√198 = 5.82847668325146
3√199 = 5.838272460814
3√200 = 5.84803547642573

B. 328平方米等于多少亩

328平方米等于(0.492)亩
1亩=2000/3平方米
328÷2000/3
=0.492(亩)

C. 328平方根是多少

√328=18.11
回答完毕~~
有疑问请追问,无疑问请点击【采纳】~
祝学习进步~~~\(^o^)/~

D. 328o.99的平方根是多少

咨询记录 · 回答于2021-07-07

E. 三百二十八平方分米等于多少平方米

解:由1平方米=100平方分米,
得328平方分米
=328÷100平方米
=3.28平方米
328平方分米=3.28平方米

F. 开根号的计算方法(手工计算)

任意数开立方根笔算步骤如下:
1、把所求数从右往左每3位分一段分成若干段,从左往右开始计算.
2、先从最左边一段开始计算。用试算法得出这段的得数(该得数要取其立方不溢出所求数第一段上的数时的最大数)设该得数为a
3、把第一段所求数与a^3的差,在其后面按位补上第二段的数,为第二段要算的数(所求数),取一个试算数b,在计算纸的其它地方第一行写上3a^2,第二行往右移一位写上3ab,第三行往右移一位写上b^2,用竖式加法算出这三行数的和(上面两行数,相应空位补上0).用这个和乘以试算数b所得的积与该段所求数进行比较.试算出最大的b(积不溢出所求数),该数b即为第二段上的得数.把该得数写在算式相应段的上方。
4、相同的方法进行下一段的计算,所不同的是a要取前面已算出的得数,(如前面两位得数分别是1,3,a就取13,如算到第四段,前面三位数分别是1,3,5,a就取135,)试算出相应的b写在该段上方。
5、算到最后一段,如最后试算出来的余数不为0,则说明所求数的立方根不是整数,此时,用与求开方相似的方法,在该数后面补一段000,再算出的得数就是小数点后的第一位数,还有余数,再补三位0,只到余数为0或者至算至足够的小数位即可。
6、该算法写出来似乎很烦,但实际计算时并不复杂。可能会化点时间。当然,这都是在没有办法以的情况下才会用笔算进行开立方的。
希望对你有帮助。

G. 2700019开平方,是多少

结果大约是1643.1704。

√200019=1643.1704……

H. 开平方怎么算

开平方和平方是互为逆运算的。把一个数(非负)开平方就是求这个数(非负)的平方根。
开平方就是思考哪些数的平方等于这个数,则这个数开平方就等于哪些数。
例如:把4开平方――
因为2和-2的平方都等于4,所以4开平方就等于2和-2,即4的平方根是2和-2。

I. 开方计算公式

1、平方根
如果一个数的平方等于
a,那么这个数叫做a的平方根(square
root),即如果x2=a,则x叫做a的平方根,记作x=±,其中a叫被开方数.
2、平方根的性质
(1)任何一个正数的平方根有两个,它们互为相反数.如正数a的平方根是±,其中+与-恰是一对相反数;
(2)零的平方根是零,即=0;
(3)负数没有平方根.
3、算术平方根
正数a的正的平方根,叫做a的算术平方根.
4、开平方
求一个非负数的平方根的运算,叫做开平方,开平方与平方互为逆运算
.
5、立方根
如果一个数的立方等于
a,那么这个数叫做a的立方根(cube
root),即如果x3=a,则x叫做a的立方根,记作:x=.
6、立方根的性质
任何一个正数的立方根是一个正数,即a0时,0;
任何一个负数的立方根是一个负数,即a0时,0;
零的立方根仍是零,即a=0时,=0.
7、开立方
求一个数的立方根的运算叫做开立方.开立方与立方互为逆运算.
8、二次根式的定义
形如(a≥0)的式子叫二次根式.
9、二次根式有意义的取值范围
二次根式有意义的取值范围是被开方数必须是非负数
.
10、二次根式的性质
(1)≥0(a≥0),即一个非负数的算术平方根是一个非负数.
(2)(a≥0),即一个非负数的算术平方根的平方等于这个非负数.
(3),即一个数的平方的算术平方根等于这个数的绝对值.
(4)当a≥0时,,即一个非负数的算术平方根的平方等于这个数的平方的算术平方根.
(5)当a≥0时,a=,即一个非负数等于它的算术平方根的平方.
11、二次根式乘除法法则
(a≥0,b≥0),即二次根式相乘就是把被开方数相乘,根指数不变.(a≥0,b0),即二次根式相除,就是把被开方数相除,根指数不变.
12、二次根式的性质
(1)积的算术平方根的性质:(a≥0,b≥0),即积的算术平方根等于各个因式的算术平方根的积.
(2)商的算术平方根的性质:(a≥0,b0),即商的算术平方根等于被除式的算术平方根除以除式的算术平方根.
13、最简二次根式
满足条件:
(1)被开方数的因数是整数,因式是整式;
(2)被开方数不含能开得尽方的因数或因式的二次根式称为最简二次根式.
14、同类二次根式
n个二次根式化成最简二次根式以后,如果被开方数相同,这几个二次根式就叫做同类二次根式.
15、二次根式的加减法
先把二次根式化成最简二次根式,再合并同类二次根式
.
16、二次根式的混合运算
二次根式的混合运算按运算顺序和运算法则进行计算,能用乘法公式的则宜用乘法公式
.

J. 开方的计算方法

开平方运算也即是开平方后所得的数的平方即原数,也就是说开平方是平方的逆运算。
例:求256的平方根

第一步:将被开方数的整数个位起向左每隔两位划为一段,用逗号分开,分成几段,表示所求平方根是几位数。
例,第一步:将256,分成两段:
2,56
表示平方根是两位数(XY,X表是平方根十位上数,Y表示个位数)。

第二步:根据左边第一段里的数,取该数的平方根的整数部分,作为所要求的平方根求最高位上的数。
例:左边第一段数值是2,2的平方根是大约等于1.414(这些尽量要记得,100以内的,尤其是能开整数的),由于2的平方根1.414大于1和小于2,所以取整数部分是1作为所要求的平方根求最高位上的数,即所要求的平方根最高位X是1。

第三步:从第一段的数减去最高位上数的平方,在它们的差的右边写上第二段数组成第一个余数。
例:第一段数里的数是2.第二步计算出最高数是1
2减去1的平方=1
将1与第二段数(56)组成一个第一个余数:156

第四步:把第二步求得的最高位数(1)乘以20去试除第一个余数(156),取所得结果的整数部分作为第一个试商。
例: 156除以(1乘20)=7.8
第一个试商就是7

第五步:第二步求得的的最高位数(1)乘以20再加上第一个试商(7)再乘以第一个试商(7)。
(1*20+7)*7
如果:(1*20+7)*7小于等于156,则7就是平方根的第二位数.
如果:(1*20+7)*7大于156,将第一个试商7减1,即用6再计算。
由于:(1*20+6)*6=156所以,6就是第平方根的第二位数。

例:求55225的平方根
第一步:将被开方数的整数个位起向左每隔两位划为一段,用逗号分开,分成几段,表示所求平方根是几位数。
例,第一步:将55225,分成三段:
5,52,25
表示平方根是三位数(XYZ)。

第二步:根据左边第一段里的数,取该数的平方根的整数部分,作为所要求的平方根求最高位上的数。
例:左边第一段数值是5,5的平方根是(2点几)大于2和小于3,所以取整数部分是2作为所要求的平方根求最高位上的数,即所要求的平方根最高位X是2。

第三步:从第一段的数减去最高位上数的平方,在它们的差的右边写上第二段数组成第一个余数。
例:第一段数里的数是5.第二步计算出最高数是2
5减去2的平方=1
将1与第二段数(52)组成一个第一个余数:152
第四步:把第二步求得的最高位数(2)乘以20去试除第一个余数(152),取所得结果的整数部分作为第一个试商。
例: 152除以(2乘20)=3.8
第一个试商就是3

第五步:第二步求得的的最高位数(2)乘以20再加上第一个试商(3)再乘以第一个试商(3)。
(2*20+3)*3
如果:(2*20+3)*3小于等于152,则3就是平方根的第二位数.
如果:(2*20+3)*3大于152,将第一个试商3减1,即用2再计算。
由于:(2*20+3)*3小于152所以,3就是第平方根的第二位数。

第六步:用同样的方法,继续求平方根的其他各位上的数。用上一个余数减去上法中所求的积(即152-129=23),与第三段数组成新的余数(即2325)。这时再求试商,要用前面所得到的平方根的前两位数(即23)乘以20去试除新的余数(2325),所得的最大整数为新的试商。(2325/(23×20)的整数部分为5。)
7.对新试商的检验如前法。(右例中最后的余数为0,刚好开尽,则235为所求的平方根。)

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