n √n in 10 n 100 n 5.01 5.02 25.1001 125.752 2.23830 7.07814 1.71112 3.68649 7.94229 .199601 25.2004 126.506 2.24054 7.08520 1.71225 3.68894 7.94757 .199203 5.03 25.3009 127.264 2.24277 7.09225 1.71339 3.69138 7.95285 .198807 5.04 25.4016 128.024 2.24499 7.09930 1.71452 3.69383 7.95811 .198413 5.05 25.5025 128.788 2.24722 7.10634 1.71566 3.69627 7.96337 .198020 n2 n3 5.36 5.37 1 5.06 25.6036 129.554 2.24944 7.11337 1.71679 3.69871 7.96863 .197629 5.07 25.7049 130.324 2.25167 7.12039 1.71792 3.70114 7.97387 .197239 5.08 25.8064 131.097 2.25389 7.12741 1.71905 3.70358 7.9791: .196850 5.09 25.9081 131.872 2.25610 7.13442 1.72017 3.70600 7.98434 .196464 5.10 26.0100 132.651 2.25832 7.14143 1.72130 3.70843 7.98957 .196078 5.11 26.1121 133.433 2.26053 7.14843 1.72242 3.71085 5.12 26.2144 134.218 2.26274 7.15542 1.72355 3.71327 5.13 26.3169 135.006 2.26495 7.16240 1.72467 5.14 26.4196 135.797 2.26716 7.16938 1.72579 5.15 26.5225 136.591 2.26936 7.17635 1.72691 3.72051 8.01559 5.16 26.6256 137.388 2.27156 7.18331 1.72802 3.72292 8.02078 .193798 5.17 26.7289 138.188 2.27376 7.19027 1.72914 3.72532 8.02596 .193424 5.18 26.8324 138.992 2.27596 7.19722 1.73025 3.72772 8.03113 .193050 5.19 26.9361 139.798 2.27816 7.20417 1.73137 3.73012 8.03629 .192678 5.20 27.0400 140.608 2.28035 7.21110 1.73248 3.73251 8.04145 .192308 7.99479 .195695 3.71566 .194175 n 5.21 27.1441 141.421 2.28254 7.21803 1.73359 3.73490 8.0466C .191939 5.22 27.2484 142.237 2.28473 7.22496 1.73470 3.73729 8.05175 .191571 5.23 27.3529 143.056 2.28692 7.23187 1.73580 3.73968 8.05689 .191205 5.24 27.4576 143.878 2.28910 7.23878 1.73691 3.74206 8.06202 .190840 5.25 27.5625 144.703 2.29129 7.24569 1.73801 3.74443 8.06714 .190476 5.26 27.6676 145.532 2.29347 7.25259 1.73912 3.74681 8.07226 5.27 27.7729 146.363 2.29565 7.25948 1.74022 3.74918 8.07737 5.28 27.8784 147.198 2.29783 7.26636 1.74132 3.75158 8.08248 5.29 27.9841 148.036 2.30000 7.27324 1.74242 3.75392 8.08758 5.30 28.0900 148.877 2.30217 7.28011 1.74351 3.75629 8.09267 5.31 28.1961 149.721 2.30434 1.74461 3.75865 8.09776 5.32 1.74570 3.76100 8.10284 5.33 1.74680 3.76336 8.10791 5.34 1.74789 3.76571 8.11298 1.74898 3.76806 8.11804 7.28697 28.3024 150.569 2.30651 7.29383 5.35 5.41 29.2681 158.340 2.32594 7.35527 1.75549 5.42 29.3764 159.220 2.32809 7.36206 1.75657 5.43 29.4849 160.103 2.33024 7.36885 1.75765 5.44 29.5936 160.989 2.33238 7.37564 1.75873 5.45 29.7025 161.879 2.33452 7.38241 1.75981 .190114 .189753 .188324 .187970 .187617 .187266 28.7296 28.8369 5.38 28.9444 5.39 5.40 .186916 153.991 2.31517 7.32120 1.75007 3.77041 8.12310 .186567 154.854 2.31733 7.32803 1.75116 3.77275 8.12814 .186220 155.721 2.31948 7.33485 1.75224 3.77509 8.13319 .185874 29.0521 156.591 2.32164 7.34166 1.75333 3.77740 8.13822 .185529 29.1600 3.77976 8.14325 .185185 157.464 2.32379 7.34847 1.75441 .189394 .189036 .188679 3.78210 8.14828 .184843 3.78442 8.15329 .184502 3.78675 8.15831 3.78907 8.16331 .184162 .183824 3.79139 8.16831 .183486 5.46 29.8116 162.771 2.33666 7.38918 1.76088 3.79371 8.17330 .183150 5.47 29.9209 163.667 2.33880 7.39594 1.76196 3.79603 8.17829 .182815 5.48 30.0304 164.567 2.34094 7.40270 1.76303 3.79834 8.18327 .182482 5.49 30.1401 165.469 2.34307 7.40945 5,50 30.2500 166.375 2.34521 7.41620 1.76410 3.80065 8.18824 .182149 1.76517 3.80295 8.19321 .181818 5.56 5.57 5.58 5.59 5.60 n2 n3 V10 n In V10 n 100 n 1.76624 3.80526 8.19818 .181488 1.76731 3.80756 8.20313 .181159 1.76838 3.80986 8.20808 .180832 1.76944 3.80115 8.21303 .180505 1.77051 3.81444 8.21797 .180180 30.9136 171.880 2.35797 7.45654 1.77157 3.81673 8.22290 .179856 31.0249 172.809 2.36008 7.46324 1.77263 3.81902 8.22783 .179533 31.1364 173.741 2.36220 7.46994 1.77369 3.82130 31.2481 174.677 2.36432 7.47663 1.77475 3.82358 31.3600 175.616 2.36643 7.48331 1.77581 3.82586 5.61 31.4721 176.558 2.36854 7.48999 5.62 31.5844 177.504 2.37065 7.49667 5.63 31.6969 178.454 2.37276 7.50333 5.64 31.8096 179.406 2.37487 7.50999 1.78003 3.83495 5.65 31.9225 180.362 2.37697 7.51665 1.78108 3.83721 1.77686 3.82814 8.24747 .178253 1.77792 3.83041 8.25237 .177936 1.77897 3.83268 8.25726 .177620 8.26215 .177305 8.26703 .176991 1 n 8.23275.179212 5.66 32.0356 181.321 2.37908 7.52330 1.78213 3.83948 8.27190 5.80 33.6400 195.112 2.40832 7.61577 1.79670 3.87088 8.23766 .178891 8.24257 .178571 5.81 33.7561 196.123 2.41039 7.62234 1.79773 3.87310 5.82 33.8724 197.137 2.41247 7.62889 1.79876 3.87532 5.83 33.9889 198.155 2.41454 7.63544 1.79979 3.87754 5.84 34.1056 199.177 2.41661 7.64199 1.80082 3.87975 5.85 34.2225 200.202 2.41868 7.64853 1.80185 3.88197 .176678 .176367 .176056 .175747 8.27677 8.28164 1.78527 3.84625 8.28649 1.78632 3.84850 8.29134 .175439 1.78736 3.85075 8.29619 .175131 1.78840 3.85300 8.30103 .174825 1.78944 3.85524 8.30587 .174520 1.79048 3.85748 8.31069 .174216 1.79152 3.85972 8.31552 .173913 1.79256 3.86196 8.32034 .173611 1.79360 3.86419 8.32515 .173310 1.79463 3.86642 8.32995 .173010 3.86865 8.33476 .172712 8.33955172414 8.34434 .172117 .171821 8.36345.170940 5.86 34.3396 201.230 2.42074 7.65506 1.80288 3.88418 8.36821 .170649 5.87 34.4569 202.262 2.42281 7.66159 1.80390 3.88639 8.37297 .170358 5.88 34.5744 203.297 2.42487 7.66812 1.80492 3.88859 8.37772 .170068 5.89 34.6921 204.336 2.42693 7.67463 1.80595 3.89082 8.38247 .169779 5.90 34.8100 205.379 2.42899 7.68115 1.80697 3.89300 8.38721 .169492 5.91 34.9281 206.425 2.43105 7.68765 1.80799 3.89520 8.39194 .169205 5.92 35.0464 207.475 2.43311 7.69415 1.80901 3.89739 8.39667 .168919 5.93 35.1649 208.528 2.43516 7.70065 1.81003 3.89958 8.40140 .168634 5.94 35.2836 209.585 2.43721 7.70714 1.81104 3.90177 8.40612 .168350 5.95 35.4025 210.645 2.43926 7.71362 1.81206 3.90396 8.41083 .168067 5.96 35.5216 211.709 2.44131 7.72010 1.81307 3.90615 8.41554 .167785 5.97 35.6409 212.776 2.44336 7.72658 1.81409 3.90833 8.42025 .167504 5.98 35.7604 213.847 2.44540 7.73305 1.81510 3.91051 8.42494 .167224 5.99 35.8801 214.922 2.44745 7.73951 1.81611 3.91269 8.42964 .166945 6.00 36.0000 216.000 2.44949 7.74597 1.81712 3.91487 8.43433 .166667 n Vn V10 n in 10 n 100 n .165563 6.01 36.1201 217.082 2.45153 7.75242 1.81813 3.91704 8.43901 6.02 36.2404 218.167 2.45357 7.75887 1.81914 3.91921 8.44369 6.03 36.3609 219.256 2.45561 7.76531 1.82014 3.92138 8.44836 6.04 36.4816 220.349 2.45764 7.77174 1.82115 3.92355 8.45303 6.05 36.6025 221.445 2.45967 7.77817 1.82215 3.92571 8.45769 .165289 6.06 36.7236 222.545 2.46171 7.78460 1.82316 6.07 36.8449 223.649 2.46374 7.79102 1.82416 6.08 36.9664 224.756 2.46577 7.79744 1.82516 6.09 37.0881 225.867 2.46779 7.80385 1.82616 6.10 37.2100 226.981 2.46982 7.81025 1.82716 6.11 6.12 6.13 n2 n3 6.16 37.9456 233.745 2.48193 7.84857 1.83313 6.17 38.0689 234.885 2.48395 7.85493 1.83412 6.18 38.1924 236.029 2.48596 7.86130 1.83511 6.19 38.3161 237.177 2.48797 7.86766 1.83610 6.20 38.4400 238.328 2.48998 1.83709 7.87401 6.21 38.5641 239.483 2.49199 7.88036 6.22 38.6884 240.642 2.49399 7.88670 6.23 38.8129 241.804 2.49600 7.89303 6.24 38.9376 242.971 2.49800 7.89937 6.25 39.0625 244.141 2.50000 7.90569 37.3321 228.099 2.47184 7.81665 1.82816 3.93865 0.48556 .163666 37.4544 229.221 2.47386 7.82304 1.82915 3.94079 8.49018 .163399 37.5769 230.346 2.47588 7.82943 1.83015 6.14 37.6996 231.476 2.47790 7.83582 1.83115 3.94294 8.49481 .163132 5.94508 8.49942 .162866 37.8225 232.608 2.47992 7.84219 1.83214 3.94722 8.50404 6.15 .162602 3.94936 8.50864 .162338 3.95150 8.51324 .162075 3.95363 8.51784 .161812 3.95576 8.52243 3.95789 8.52702 .161551 .161290 1.83808 3.96002 8.53160 3.97062 8,55444 6.26 39.1876 245.314 2.50200 7.91202 1.84300 6.29 39.5641 248.858 2.50799 7.93095 1.84594 3.97695 8.56808 6.30 39.6900 250.047 2.50998 7.93725 1.84691 3.97906 8.57262 2.513967.94984 3.92787 8.46235 .165017 3.93003 8.46700 .164745 3.93219 8.47165 .164474 3.93434 8.47629 .164204 3.93650 8.48093 .163934 1 3.972738.55899 6.31 39.8161 251.240 2.51197 7.94355 1.84789 3.98116 8.57715 6.33 40.0689 253.636 2.51595 7.95613 1.84984 3,98536 8.58620 n 6.36 40.4496 257.259 2.52190 7.97496 1.85276 3.99165 .166389 .166113 .165838 .159744 .159490 3.97484 8.56354 .159236 .158983 .158730 .161031 .160772 .160514 .160256 .160000 .158479 .158228 .157978 .157729 .157480 8.59975 .157233 8.60425 .156986 8.60875.156740 8.61325 156495 8.61774 156250 4.00208 8.62222 1.156006 4.00416 8.62671 .155763 1.85953 4.00624 8.63118 .155521 1.86050 4.00×32 8.63566 155280 1.86146 4.01039 8.64012 .155039 6.46 41.7316 269.586 2.54165 8.03741 1.862424.01246 8.64459 .154799 6.49 1.86530 6.50 4.01866 8.65795 .154083 4.02073 8.66239 .153846 6.71 6.72 6.73 6.74 6.75 6.56 43.0336 282.300 2.56125 8.09938 8.11172 V10 n Vn V10 n V100 n 1.86721 4.02279 8.66683 .153610 1.86817 4.02485 8.67127 .153374 1.86912 4.02690 8.67570 .153139 1.87008 4.02896 8.68012 .152905 1.87103 4.03101 8.68455 .152672 6.61 43.6921 288.805 2.57099 8.13019 1.87672 4.04328 8.71098 .151286 6.62 43.8244 290.118 2.57294 8.13634 1.87767 4.04532 8.71537 .151057 6.63 43.9569 291.434 2.57488 8.14248 1.87862 4.04735 8.71976 .150830 6.64 44.0896 292.755 2.57682 8.14862 1.87956 4.04939 8.72414 .150602 6.65 44.2225 294.080 2.57876 8.15475 1.88050 4.05142 8.72852 .150376 6.66 44.3556 295.408 2.58070 8.16088 1.88144 4.05345 8.73289 .150150 6.67 44.4889 296.741 2.58263 8.16701 1.88239 4.05548 8.73726 .149925 6.68 44.6224 298.078 2.58457 8.17313 1.88333 4.05750 8.74162 .149701 6.69 44.7561 299.418 2.58650 8.17924 1.88427 4.05953 8.74598 6.70 44.8900 300.763 2.58844 8.18535 1.88520 4.06155 8.75034 .149477 .149254 45.0241 302.112 2.59037 8.19146 1.88614 4.06357 8.75469 8.76772 8.77205 6.81 46.3761 315.821 2.60960 8.25227 6.82 46.5124 317.215 2.61151 8.25833 6.83 46.6489 318.612 2.61343 8.26438 6.84 46.7856 320,014 2.61534 8.27043 6.85 46.9225 321.419 2.61725 8.27647 8.68896 .152439 8.69338 .152207 1.87198 4.03306 8.69778 .151976 8.70219 .151745 6.76 45.6976 308.916 2.60000 8.22192 1.89081 4.07364 6.96 48.4410 n 1.89546 4.08365 8.79797 6.86 47.0596 322.829 2.61916 8.28251 2.63439 8.33067 1.90745 4.10948 8.77638 .147929 8.78071 .147711 1.89268 4.07765 8.78503 1.89361 4.07965 8.78935 1.89454 4.08166 8.79366 .147493 .147275 .147059 .149031 .148810 .148588 .148368 .148148 1.90009 4.09362 8.81945 .145773 .145349 .144928 8.86210 337.154 2.63818 8.34266 1.90928 4.11342 .146843 .146628 .146413 .146199 .145985 .144718 .144509 .144300 8.85360 .144092 8.85785 .143885 .143678 .143472 4.11736 8.87058 .143267 8.36062 1.91202 4.11932 8.87481 .143062 8.36660 1.91293 4.12129 8.87904 .142857 n √n 110 η 7.01 49.1401 344.472 2.64764 8.37257 7.02 49.2804 345.948 2.64953 8.37854 7.03 49.4209 347.429 2.65141 8.38451 7.04 49.5616 348.914 2.65330 8.39047 7.05 49.7025 350.403 2.65518 8.39643 n2 n3 7.06 49.8436 351.896 2.65707 8.40238 1.91838 7.08 in 10 n 100 n 1.91384 4.12325 8.88327 .142653 4.13303 8.90434 .141643 4.13498 8.90854 .141443 4.13695 8.91274 .141243 4.13887 8.91693 .141044 4.14082 8.92112 .140845 .140647 1.92290 4.14276 8.92531 .139860 .139665 .139470 7.16 51.2656 367.062 2.67582 8.46168 1.92740 4.15245 8.94618 7.17 51.4089 368.602 2.67769 8.46759 1.92829 4.15438 8.95034 7.18 51.5524 370.146 2.67955 8.47349 1.92919 4.15631 8.95450 .139276 7.19 51.6961 371.695 2.68142 8.47939 1.93008 4.15824 8.95866 .139082 7.20 51.8400 373.248 2.68328 8.48528 1.93098 4.16017 8.96281 .138889 1.93633 4.17169 7.26 52.7076 382.657 2.69444 8.52056 1.93810 4.17552 7.30 53.2900 389.017 2.70185 8.54400 1.93988 4.17934 9.00411 4.18125 .00822 7.31 53.4361 390.618 2.70370 8.54985 1.94076 7.21 51.9841 374.805 2.68514 8.49117 1.93187 4.16209 3.96696 .138696 7.22 52.1284 376.367 2.68701 8.49706 1.93277 4.16402 8.97110 .138504 7 23 52.2729 377.933 2.68887 8.50294 1.93366 4.16594 8.97524 .138313 7.24 52.4176 379.503 2.69072 8.50882 1.93455 4.16786 7.25 52.5625 381.078 2.69258 8.51469 1.93544 4.16978 8.97938 .138122 8.98351 .137931 7.46 7.47 7.48 55.8009 416.833 2.73313 8.64292 55.9504 418.509 2.73496 8.64870 56.1001 420.190 2.73679 8.65448 7.50 56.2500 421.875 2.73861 8.66025 7.49 1 7.36 54.1696 398.688 2.71293 8.57904 7.38 54.4644 401.947 2.71662 8.59069 1.94694 4.19455 1.94782 4.19644 n 4.183159.01233 55.6516 415.161 2.73130 2.63713 1.95395 4.20965 1.95569 1.95656 1.95743 8.98764.137741 8.99176.137552 4.18506 9,01643 8.99588 .137363 9.00000 137174 .136986 .136799 .136612 .136426 .136240 9.02462 136054 1.94518 4.19076 9.02871 + 135870 1.94606 4.19266 9.03280 .135685 7.43 7.41 54.9081 406.869 2.72213 8.60814 1.94957 4.20023 7.42 55.0564 408.518 2.72397 8.61394 1.95045 4.20212 9.05318 .134771 55.2049 410.172 2.72580 8.61974 1.95132 4.20400 9.05725 134590 55.3536 411.831 2.72764 8.62554 1.95220 4.20589 9.06131 .134409 55.5025 413.494 2.72947 8.63134 1.95307, 4.20777 9.06537 134228 7.44 7.45 9.03689.135501 9.04097 135318 9.04504 135135 9.04911.134953 9.06942 .134048 1.95482 4.21153 9.07347 .133869 4.21341 9.07752 .133690 4.21529 9.08156 .133511 4.21716.08560.133333 |