The following is a list of all the integers from -50 to 50 which have square roots expressible in various number bases. It's followed by the right-most digits of the square roots of these numbers. The x's indicate digits which are ambiguous given the precision.
Observations on the square roots.00000000000000000000000000000001 1 x0000000000000000000000000000001 x1111111111111111111111111111111 --- 00000000000000000000000000000100 4 xx000000000000000000000000000010 xx111111111111111111111111111110 --- 00000000000000000000000000001001 9 x1111111111111111111111111111101 x0000000000000000000000000000011 --- 00000000000000000000000000010000 16 xxx00000000000000000000000000100 xxx11111111111111111111111111100 --- 00000000000000000000000000010001 17 x0110011110100110010011011101001 x1001100001011001101100100010111 --- 00000000000000000000000000011001 25 x0000000000000000000000000000101 x1111111111111111111111111111011 --- 00000000000000000000000000100001 33 x0100101101111010110011110010001 x1011010010000101001100001101111 --- 00000000000000000000000000100100 36 xx111111111111111111111111111010 xx000000000000000000000000000110 --- 00000000000000000000000000101001 41 x0000000110011000110011011001101 x1111111001100111001100100110011 --- 00000000000000000000000000110001 49 x1111111111111111111111111111001 x0000000000000000000000000000111 --- 11111111111111111111111111111001 -7 x0011100100110001100000010110101 x1100011011001110011111101001011 --- 11111111111111111111111111110001 -15 x1111101111011100100010011011001 x0000010000100011011101100100111 --- 11111111111111111111111111101001 -23 x1110011110110010110110000101101 x0001100001001101001001111010011 --- 11111111111111111111111111100100 -28 xx111001001100011000000101101010 xx000110110011100111111010010110 --- 11111111111111111111111111100001 -31 x0100011101000010101011101110001 x1011100010111101010100010001111 --- 11111111111111111111111111011001 -39 x0110100101110110111110001100101 x1001011010001001000001110011011 --- 11111111111111111111111111010001 -47 x0100011010111110010100111001001 x1011100101000001101011000110111
00000000000000000000000000000001 1 00000000000000000000000000000001 22222222222222222222222222222222 --- 00000000000000000000000000000011 4 22222222222222222222222222222221 00000000000000000000000000000002 --- 00000000000000000000000000000021 7 21102101210121201222021120020111 01120121012101021000201102202112 --- 00000000000000000000000000000100 9 x0000000000000000000000000000010 x2222222222222222222222222222220 --- 00000000000000000000000000000101 10 22102220121101002211102100121201 00120002101121220011120122101022 --- 00000000000000000000000000000111 13 22120000112100012222012112100121 00102222110122210000210110122102 --- 00000000000000000000000000000121 16 00000000000000000000000000000011 22222222222222222222222222222212 --- 00000000000000000000000000000201 19 11211022122222012010211200110101 11011200100000210212011022112122 --- 00000000000000000000000000000211 22 01221211002112021101102202221021 21001011220110201121120020001202 --- 00000000000000000000000000000221 25 22222222222222222222222222222211 00000000000000000000000000000012 --- 00000000000000000000000000001001 28 10011012101202112001102212112001 12211210121020110221120010110222 --- 00000000000000000000000000001011 31 00110101011022001202010221201221 22112121211200221020212001021002 --- 00000000000000000000000000001021 34 20201021122112010020021010012111 02021201100110212202201212210112 --- 00000000000000000000000000001100 36 x2222222222222222222222222222210 x0000000000000000000000000000020 --- 00000000000000000000000000001101 37 00220002012011210222222210210201 22002220210211012000000012012022 --- 00000000000000000000000000001111 40 01010011210020210100011021202121 21212211012202012122211201020102 --- 00000000000000000000000000001121 43 22221000100022020122220220122011 00001222122200202100002002100212 --- 00000000000000000000000000001201 46 10101210101121210011012101022101 12121012121101012211210121200122 --- 00000000000000000000000000001211 49 00000000000000000000000000000021 22222222222222222222222222222202 --- 22222222222222222222222222222221 -2 00022211102201101021200010200211 22200011120021121201022212022012 --- 22222222222222222222222222222211 -5 00001222022212212000101221212021 22221000200010010222121001010202 --- 22222222222222222222222222222201 -8 22100100010120020102122201121101 00122122212102202120100021101122 --- 22222222222222222222222222222121 -11 22002111121100210211111011101011 00220111101122012011111211121212 --- 22222222222222222222222222222111 -14 20121221222102021211201011221121 02101001000120201011021211001102 --- 22222222222222222222222222222101 -17 01000111210110000101101122102201 21222111012112222121121100120022 --- 22222222222222222222222222222100 -18 x0222111022011010212000102002110 x2000111200211212010222120220120 --- 22222222222222222222222222222021 -20 22212001100020021222012002021111 00010221122202201000210220201112 --- 22222222222222222222222222222011 -23 00101022102011210211120110020221 22121200120211012011102112202002 --- 22222222222222222222222222222001 -26 02212212222121221011210212111001 20010010000101001211012010111222 --- 22222222222222222222222222221221 -29 20121001020120222102001100101211 02101221202102000120221122121012 --- 22222222222222222222222222221211 -32 01022022201212112010200112210021 21200200021010110212022110012202 --- 22222222222222222222222222221201 -35 12102222110002021202202111202101 10120000112220201020020111020122 --- 22222222222222222222222222221121 -38 02200221201201111010211101202011 20022001021021111212011121020212 --- 22222222222222222222222222221111 -41 01102102110011001220110020112121 21120120112211221002112202110102 --- 22222222222222222222222222221101 -44 01210222210021101100000200020201 21012000012201121122222022202022 --- 22222222222222222222222222221100 -45 x0012220222122120001012212120210 x2210002000100102221210010102020 --- 22222222222222222222222222221021 -47 20012122102220001100102200022111 02210100120002221122120022200112 --- 22222222222222222222222222221011 -50 21100211211102002120122022111221 01122011011120220102100200111002
00000000000000000000000000000001 1 x0000000000000000000000000000001 x3333333333333333333333333333333 --- 00000000000000000000000000000010 4 x0000000000000000000000000000002 x3333333333333333333333333333332 --- 00000000000000000000000000000021 9 x3333333333333333333333333333331 x0000000000000000000000000000003 --- 00000000000000000000000000000100 16 xx000000000000000000000000000010 xx333333333333333333333333333330 --- 00000000000000000000000000000101 17 x0112202100133030303310302123221 x3221131233200303030023031210113 --- 00000000000000000000000000000121 25 x0000000000000000000000000000011 x3333333333333333333333333333323 --- 00000000000000000000000000000201 33 x3022021031100130211233112132101 x0311312302233203122100221201233 --- 00000000000000000000000000000210 36 x0000000000000000000000000000012 x3333333333333333333333333333322 --- 00000000000000000000000000000221 41 x1230202122333320000303012123031 x2103131211000013333030321210303 --- 00000000000000000000000000000301 49 x3333333333333333333333333333321 x0000000000000000000000000000013 --- 33333333333333333333333333333321 -7 x1212310232312032130212030002311 x2121023101021301203121303331023 --- 33333333333333333333333333333301 -15 x2330202211120001331323210103121 x1003131122213332002010123230213 --- 33333333333333333333333333333221 -23 x0103303233301013303312112300231 x3230030100032320030021221033103 --- 33333333333333333333333333333210 -28 x0302112202103203012303213322112 x3031221131230130321030120011222 --- 33333333333333333333333333333201 -31 x2133222003313100203220111131301 x1200111330020233130113222202033 --- 33333333333333333333333333333121 -39 x2033202112220100310232313301211 x1300131221113233023101020032123 --- 33333333333333333333333333333101 -47 x1303313232320312203113302213021 x2030020101013021130220031120313
00000000000000000000000000000001 1 00000000000000000000000000000001 44444444444444444444444444444444 --- 00000000000000000000000000000004 4 00000000000000000000000000000002 44444444444444444444444444444443 --- 00000000000000000000000000000011 6 33000210413342223233033132124031 11444234031102221211411312320414 --- 00000000000000000000000000000014 9 44444444444444444444444444444442 00000000000000000000000000000003 --- 00000000000000000000000000000021 11 20231012244200433234102330200211 24213432200244011210342114244234 --- 00000000000000000000000000000024 14 32334231014323332121341141404132 12110213430121112323103303040313 --- 00000000000000000000000000000031 16 44444444444444444444444444444441 00000000000000000000000000000004 --- 00000000000000000000000000000034 19 42402023042130301142213311101022 02042421402314143302231133343423 --- 00000000000000000000000000000041 21 00403241112230041044003131103321 44041203332214403400441313341124 --- 00000000000000000000000000000044 24 21000421332240002021121314303112 23444023112204442423323130141333 --- 00000000000000000000000000000100 25 x0000000000000000000000000000010 x4444444444444444444444444444440 --- 00000000000000000000000000000101 26 30444022322342330231300401302301 14000422122102114213144043142144 --- 00000000000000000000000000000104 29 41131431344002411011342343143402 03313013100442033433102101301043 --- 00000000000000000000000000000111 31 00341221220320130424412414022331 44103223224124314020032030422114 --- 00000000000000000000000000000114 34 42402420132321412131102412300342 02042024312123032313342032144103 --- 00000000000000000000000000000121 36 00000000000000000000000000000011 44444444444444444444444444444434 --- 00000000000000000000000000000124 39 10221312212121000014343030042032 34223132232323444430101414402413 --- 00000000000000000000000000000131 41 24403111404412243424340212010241 20041333040032201020104232434204 --- 00000000000000000000000000000134 44 41012030043401422023210210400422 03432414401043022421234234044023 --- 00000000000000000000000000000141 46 21340011433240444101240232140121 23104433011204000343204212304324 --- 00000000000000000000000000000144 49 00000000000000000000000000000012 44444444444444444444444444444433 --- 44444444444444444444444444444444 -1 31141421404340423140223032431212 13303023040104021304221412013233 --- 44444444444444444444444444444441 -4 32111101130213043113443324032021 12333343314231401331001120412424 --- 44444444444444444444444444444434 -6 13110332442323243131001342321122 31334112002121201313443102123323 --- 44444444444444444444444444444431 -9 44030320224122330021224203344141 00414124220322114423220241100304 --- 44444444444444444444444444444424 -11 04424242412133202041302311441232 40020202032311242403142133003213 --- 44444444444444444444444444444421 -14 03333101413101233330104023210411 41111343031343211114340421234034 --- 44444444444444444444444444444414 -16 14222202310431141232442203114042 30222242134013303212002241330403 --- 44444444444444444444444444444411 -19 00241012214304441201122024440231 44203432230140003243322420004214 --- 44444444444444444444444444444404 -21 44431211030213113014003024421102 00013233414231331430441420023343 --- 44444444444444444444444444444401 -24 13223224004242403132441204302201 31221220440202041312003240142244 --- 44444444444444444444444444444400 -25 x1414214043404231402230324312120 x3030230401040213042214120132330 --- 44444444444444444444444444444344 -26 14202441441133113002331321424312 30242003003311331442113123020133 --- 44444444444444444444444444444341 -29 40102100111000314212011440020221 04342344333444130232433004424224 --- 44444444444444444444444444444334 -31 01203340034401334222003432111222 43241104410043110222441012333223 --- 44444444444444444444444444444331 -34 31224040434042401300110202203341 13220404010402043144334242241104 --- 44444444444444444444444444444324 -36 43111141003300210043003412243332 01333303441144234401441032201113 --- 44444444444444444444444444444321 -39 20210003224131234032244103031111 24234441220313210412200341413334 --- 44444444444444444444444444444314 -41 33234134343423031010000404203142 11210310101021413434444040241303 --- 44444444444444444444444444444311 -44 30040404120123040311334321011431 14404040324321404133110123433014 --- 44444444444444444444444444444304 -46 21233303421134320224442310012202 23211141023310124220002134432243 --- 44444444444444444444444444444301 -49 20141332031303311211212444214401 24303112413141133233232000230044
00000000000000000000000000000001 1 x0000000000000000000000000000001 x2400101400112523201211112415131 x3155454155443032354344443140425 x5555555555555555555555555555555 --- 00000000000000000000000000000004 4 xx000000000000000000000000000002 xx200203200225450402422225234302 xx355352355330105153133330321254 xx555555555555555555555555555554 --- 00000000000000000000000000000013 9 x0000000000000000000000000000003 x3555250555213141551522213502123 x2000305000342414004033342053433 x5555555555555555555555555555553 --- 00000000000000000000000000000024 16 xxx55145155100214350311101042552 xxx55555555555555555555555555552 xxx00000000000000000000000000004 xxx00410400455341205244454513004 --- 00000000000000000000000000000041 25 x4355043354543251145055544223421 x5555555555555555555555555555551 x0000000000000000000000000000005 x1200512201012304410500011332135 --- 00000000000000000000000000000100 36 xx000000000000000000000000000010 xx001014001125232012111124151310 xx554541554430323543444431404250 xx555555555555555555555555555550 --- 00000000000000000000000000000121 49 x0000000000000000000000000000011 x0401115401242155213322241010441 x5154440154313400342233314545115 x5555555555555555555555555555545 --- 55555555555555555555555555555521 -23 x1305414334453124041141323213511 x1144140521521322521141131011341 x4411415034034233034414424544215 x4250141221102431514414232342045 --- 55555555555555555555555555555441 -47 x4505330453212200211403422022321 x0445200542510400415133202311451 x5110355013045155140422353244105 x1050225102343355344152133533235
00000000000000000000000000000001 1 00000000000000000000000000000001 66666666666666666666666666666666 --- 00000000000000000000000000000002 2 54365536623164112011266421216213 12301130043502554655400245450454 --- 00000000000000000000000000000004 4 00000000000000000000000000000002 66666666666666666666666666666665 --- 00000000000000000000000000000011 8 24602260120305442644100524231241 42064406546361224022566142435426 --- 00000000000000000000000000000012 9 00000000000000000000000000000003 66666666666666666666666666666664 --- 00000000000000000000000000000014 11 44622351514640346621513144334422 22044315152026320045153522332245 --- 00000000000000000000000000000021 15 25352303062542642544562343420311 41314363604124024122104323246356 --- 00000000000000000000000000000022 16 66666666666666666666666666666663 00000000000000000000000000000004 --- 00000000000000000000000000000024 18 26463246502555336034165563654642 40203420164111330632501103012025 --- 00000000000000000000000000000031 22 06256366132404623212555030020151 60410300534262043454111636646516 --- 00000000000000000000000000000032 23 00646610331123610344604553401153 66020056335543056322062113265514 --- 00000000000000000000000000000034 25 66666666666666666666666666666662 00000000000000000000000000000005 --- 00000000000000000000000000000041 29 12160125334234560542255403543521 54506541332432106124411263123146 --- 00000000000000000000000000000042 30 45634264160560302151254460265543 21032402506106364515412206401124 --- 00000000000000000000000000000044 32 52504550240614215621201351462512 14162116426052451045465315204155 --- 00000000000000000000000000000051 36 66666666666666666666666666666661 00000000000000000000000000000006 --- 00000000000000000000000000000052 37 45036626604155060333416300461433 21630040062511606333250366205234 --- 00000000000000000000000000000054 39 44254603310204066014005236505132 22412063356462600652661430161535 --- 00000000000000000000000000000061 43 16410535305001416103322546425631 50256131361665250563344120241036 --- 00000000000000000000000000000062 44 44121633334055640123340344664523 22545033332611026543326322002144 --- 00000000000000000000000000000064 46 02430165255355664530143433156252 64236501411311002136523233510415 --- 00000000000000000000000000000100 49 x0000000000000000000000000000010 x6666666666666666666666666666660 --- 00000000000000000000000000000101 50 01560656352246563060065036423401 65106010314420103606601630243266 --- 66666666666666666666666666666664 -3 26503502530430542412446511256052 40163164136236124254220155410615 --- 66666666666666666666666666666662 -5 62223621022002000635410425112623 04443045644664666031256241554044 --- 66666666666666666666666666666661 -6 40435634111546233416006301140231 26231032555120433250660365526436 --- 66666666666666666666666666666654 -10 22355442105640600351236062122632 44311224561026066315430604544035 --- 66666666666666666666666666666652 -12 10356361305505251541440344121533 56310305361161415125226322545134 --- 66666666666666666666666666666651 -13 22604113222554640235132211416261 44062553444112026431534455250406 --- 66666666666666666666666666666644 -17 52026632451544253365115064235312 14640034215122413301551602431355 --- 66666666666666666666666666666642 -19 44552205336100126260226045320643 22114461330566540406440621346024 --- 66666666666666666666666666666641 -20 12216124622662665062545513441121 54450542044004001604121153225546 --- 66666666666666666666666666666634 -24 11204601223425500135015602310462 55462065443241166531651064356205 --- 66666666666666666666666666666632 -26 16016453050115200343052034365253 50650213616551466323614632301414 --- 66666666666666666666666666666631 -27 50552555445044406125660532532451 16114111221622260541006134134216 --- 66666666666666666666666666666624 -31 06602343311135422352135522343442 60064323355531244314531144323225 --- 66666666666666666666666666666622 -33 60626215124432540402645611316063 06040451542234126264021055350604 --- 66666666666666666666666666666621 -34 40253412036440351640533106220611 26413254630226315026133560446056 --- 66666666666666666666666666666614 -38 64051560065510621340656606111222 02615106601156045326010060555445 --- 66666666666666666666666666666612 -40 21622452452055165634161512421103 45044214214611501032505154245564 --- 66666666666666666666666666666611 -41 25446445436353204460454103356541 41220221230313462206212563310126 --- 66666666666666666666666666666604 -45 50004463066006002542531611341502 16662203600660664124135055325165 --- 66666666666666666666666666666602 -47 00556446205664341520430131622313 66110220461002325146236535044354 --- 66666666666666666666666666666601 -48 45620614052353133253455645423301 21046052614313533413211021243366
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