平方根表(square root table)常用数表之一即一元实函数y= J丁的函数值表.平方根表有多种，其查法各异，一般都在表后加以说明.

中文名

平方根表

外文名

The square root list

别    名

二次方根正数平方根

一个正数有两个平方根

负数平方根

负数没有平方根

特    殊

0只有一个平方根，就是0本身

平方根表平方根

编辑

语音

平方根，是指自乘结果等于的实数，表示为±(√x)，读作正负根号下x或x的平方根。其中的非负数的平方根称为算术平方根。正整数的平方根通常是无理数。定义：在分数指数中，依定义，可知开平方运算对乘法满足分配律，即：注意若n是非负实数且时，因为必定是正数，但有正负两个解。 应等于±；即(见绝对值)。

图1平方根若一个数x，它的的平方等于a，即x²=a,

若x的平方等于a，那么x就叫做a的平方根，即√a￣=x

像加减乘除一样，求平方根也有自己的竖式运算。以求3的算术平方根为例，过程如图1：解得3的算术平方根约为1.732

平方根1、因为每次补数需要补两位，所以被开方数不只一个数位时，要保证补数不能夹着小数点。例如三位数，必须单独用百位进行运算，补数时补上十位和个位的数。

2、每一个过渡数都是由上一个过渡数变化而后，上一个过渡数的个位数乘以2，如果需要进位，则往前面进1，然后个位升十位，以此类推，而个位上补上新的运算数字。简单地讲，过渡数27.，是第一次商的1乘以20，把个位上的0用第二次商的7来换，过渡数343是前两次商的17乘以20=340，其中个位0用第三次商的3来换，第三个过渡数3462是前三次商173乘以20=3460，把个位0用第四次的商2来换，依次类推。

3、误差值的作用。如果要求精确到更高的小数数位，可以按规则，对误差值继续进行运算。

平方根表常用平方根

编辑

语音

√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[1]

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参考资料

1.

谈高等数学中的算术平方根

．维普期刊[引用日期2017-10-08]