根号2的计算(根号3等)(开方计算的方法，精确到小数点后N位数)e的数值π的数值(精确到小数点后N位数) 开方的具体计算方法.比如15怎么开到小数点后两位
\u6839\u53f72\u52a0\u6839\u53f73\u7b49\u4e8e\u6839\u53f7\u51e0\u6839\u53f72\u548c\u6839\u53f73\u90fd\u4e3a\u65e0\u7406\u6570\uff0c\u6240\u4ee5\u76f8\u52a0\u7684\u6700\u7b80\u5f62\u5f0f\u4e3a\uff1a\u221a2+\u221a3
\u5c0f\u6570\u5f62\u5f0f\u4e3a\uff1a=3.1462643699419723423291350657156\u3002
\u62d3\u5c55\u5185\u5bb9\uff1a\u65e0\u7406\u6570\uff0c\u4e5f\u79f0\u4e3a\u65e0\u9650\u4e0d\u5faa\u73af\u5c0f\u6570\uff0c\u4e0d\u80fd\u5199\u4f5c\u4e24\u6574\u6570\u4e4b\u6bd4\u3002\u82e5\u5c06\u5b83\u5199\u6210\u5c0f\u6570\u5f62\u5f0f\uff0c\u5c0f\u6570\u70b9\u4e4b\u540e\u7684\u6570\u5b57\u6709\u65e0\u9650\u591a\u4e2a\uff0c\u5e76\u4e14\u4e0d\u4f1a\u5faa\u73af\u3002 \u5e38\u89c1\u7684\u65e0\u7406\u6570\u6709\u975e\u5b8c\u5168\u5e73\u65b9\u6570\u7684\u5e73\u65b9\u6839\u3001\u03c0\u548ce\uff08\u5176\u4e2d\u540e\u4e24\u8005\u5747\u4e3a\u8d85\u8d8a\u6570\uff09\u7b49\u3002\u65e0\u7406\u6570\u7684\u53e6\u4e00\u7279\u5f81\u662f\u65e0\u9650\u7684\u8fde\u5206\u6570\u8868\u8fbe\u5f0f\u3002\u65e0\u7406\u6570\u6700\u65e9\u7531\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b66\u6d3e\u5f1f\u5b50\u5e0c\u4f2f\u7d22\u65af\u53d1\u73b0\u3002
\u5728\u6570\u5b66\u4e2d\uff0c\u65e0\u7406\u6570\u662f\u6240\u6709\u4e0d\u662f\u6709\u7406\u6570\u5b57\u7684\u5b9e\u6570\uff0c\u540e\u8005\u662f\u7531\u6574\u6570\u7684\u6bd4\u7387\uff08\u6216\u5206\u6570\uff09\u6784\u6210\u7684\u6570\u5b57\u3002\u5f53\u4e24\u4e2a\u7ebf\u6bb5\u7684\u957f\u5ea6\u6bd4\u662f\u65e0\u7406\u6570\u65f6\uff0c\u7ebf\u6bb5\u4e5f\u88ab\u63cf\u8ff0\u4e3a\u4e0d\u53ef\u6bd4\u8f83\u7684\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u4eec\u4e0d\u80fd\u201c\u6d4b\u91cf\u201d\uff0c\u5373\u6ca1\u6709\u957f\u5ea6\uff08\u201c\u5ea6\u91cf\u201d\uff09\u3002
\u53c2\u8003\u8d44\u6599\uff1a\u65e0\u7406\u6570-\u767e\u5ea6\u767e\u79d1
\u5f00\u5e73\u65b9\u662f\u4e2a\u5927\u5de5\u7a0b\uff0c\u5c31\u4ecb\u7ecd\u4e2a\u6613\u7406\u89e3\u7684\u65b9\u6cd5\u5427\uff08\u7b80\u5355\u4f46\u9ebb\u70e6\uff0c\u53ef\u4ee5\u7b97\u5230\u5410\u8840\uff09\uff1a
\u4e8c\u6b21\u65b9\u7a0b\u6709\u5b66\u8fc7\uff1f\u4e8c\u5206\u6cd5\u6709\u5b66\u8fc7\uff1f
\u5b66\u8fc7\u5c31\u597d\u529e\u4e86\uff0c\u6ca1\u5b66\u8fc7\u4e5f\u6ca1\u4e8b\uff0c\u987a\u5e26\u7ed9\u4f60\u8bb2\u4e00\u4e0b\uff1a
\u5047\u8bbe\uff0c\u4f60\u8981\u6c42\uff1a\u6839\u53f72
\u5217\u4e00\u4e2a\u65b9\u7a0b\uff1aX^2=2\uff0c\u8fd9\u4e2a\u65b9\u7a0b\u53c8\u53ef\u4ee5\u5199\u4f5c\uff1aX^2\u20142=0
\u8bbe\uff1af(x)=X^2\u20142\uff08\u8fd9\u91cc\u201df(x)\u201d\u662f\u4e2a\u7b26\u53f7\uff0c\u4f60\u4e5f\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e00\u4e2a\u666e\u901a\u7684\u5b57\u6bcd\uff0c\u81f3\u4e8e\u4e3a\u4ec0\u4e48\u8fd9\u4e48\u8bbe\u4e00\u4f1a\u4f60\u5c31\u77e5\u9053\u4e86\uff09
\u627e\u5230\u4e24\u4e2aX\u7684\u503c\uff0c\u5176\u4e2d\u4e00\u4e2a\u53ef\u4ee5\u8ba9f(x)\u5c0f\u4e8e\u96f6\uff0c\u4e00\u4e2a\u53ef\u4ee5\u8ba9f(x)\u5927\u4e8e\u96f6\u3002\u4f8b\u59821\u548c2\uff08\u4e5f\u5c31\u662f\u8bf4\u65b9\u7a0bX^2=2\u7684\u5176\u4e2d\u4e00\u4e2a\u89e3\u57281~2\u4e4b\u95f4\uff09\u3002
\u73b0\u5728\u4f60\u77e5\u9053f(1)0\u4e14\u7b49\u4e8e2\u4e86\uff08f(1)\u5c31\u4ee3\u8868\u5f0f\u5b50(X^2\u20142)\u91cc\u7684X\u53d61\u65f6\u6574\u4e2a\u5f0f\u5b50\u7684\u503c\uff0cf(2)\u540c\u7406\uff09
\u73b0\u5728\uff0c\u8981\u7528\u5230\u4e00\u5f00\u59cb\u8bf4\u7684\u4e8c\u5206\u6cd5\u4e86\u3002
\u8ba1\u7b97f[(1+2)/2]\u7684\u503c\uff0c\u4e5f\u5c31\u662f\u8ba1\u7b97f(1.5)\u7684\u503c\uff0c\u53d1\u73b0\u5176\u503c\u4e3a0.25\u4e14\u5927\u4e8e0
\u6240\u4ee5\uff0c\u6211\u4eec\u820d\u5f03\u4e4b\u524d\u7b97\u51fa\u7684\u5927\u4e8e0\u7684f(2)\uff0c\u4f60\u73b0\u5728\u77e5\u9053\u65b9\u7a0b\u7684\u89e3\u57281~1.5\u4e4b\u95f4\u4e86\u3002
\u7ee7\u7eed\u8ba1\u7b97f[(1+1.5)/2]\uff08f(1.25)\uff09\u7684\u503c\uff0c\u53d1\u73b0\u5176\u503c\u4e3a-0.4375\u5c0f\u4e8e\u96f6\uff0c\u820d\u5f03\u4e4b\u524d\u7b97\u51fa\u7684\u5c0f\u4e8e\u96f6\u7684f(1)\uff0c\u73b0\u5728\u6211\u4eec\u53c8\u77e5\u9053\u65b9\u7a0b\u7684\u89e3\u57281.25~1.5\u4e4b\u95f4\u4e86\u3002
\u6240\u4ee5\u8ba1\u7b97f[(1.25+1.5)/2]\uff08f(1.375)\uff09\u2026\u2026
\u5982\u6b64\u5f80\u590d\uff0c\u4f60\u4f1a\u53d1\u73b0\u4f60\u7b97\u51fa\u7684f(x)\u503c\u8d8a\u6765\u8d8a\u63a5\u8fd10\uff01
\u5f53\u6709\u4e00\u4e2a\u6570\u6b63\u597d\u8ba9f(x)=0\uff0c\u5c31\u8bf4\u660e\u4f60\u7b97\u51fa\u4e86\u6839\u53f72\u7684\u51c6\u786e\u6570\u503c\uff08\u5f53\u7136\u90a3\u662f\u4e0d\u53ef\u80fd\u7684\uff0c\u5bf9\u4e8e\u8fd9\u4e2a\u5f0f\u5b50\uff0c\u4f60\u53ea\u80fd\u8ba9f(x)\u65e0\u9650\u63a5\u8fd1\u4e8e0\uff0c\u5c4a\u65f6x\u7684\u503c\u5c06\u65e0\u9650\u63a5\u8fd1\u4e8e1.414213562\u2026\u2026\uff0c\u4e5f\u5c31\u662f\u6839\u53f72\u7684\u5927\u81f4\u6570\u503c\uff09
\u795d\u4f60\u7b97\u5230\u5410\u8840\uff01\u65b0\u5e74\u5feb\u4e50\uff01
开根号的手算方法是基于(A*10+B)^2=100A^2+20AB+B^2=100A^2+B(20A+B)
设根号的第一位是A,这个可以直接看出,那么第二位B要满足B(20A+B)小于并接近原数减A^2的余数
其中(20A+B)我定义为除数
开根号2的手算方法
1)首先是补0,要补精确位数乘以2个0,且如根号2保留4位小数,要补8个0
1 ___________1就是A
------------------
√2。00' 00' 00 '00'
1 ____________1是A^2
----------------------------
1 00 _____________原数与A^2的差
要把A乘以20,这里是把1乘以20，在A后面上B,B要满足B(20A+B)<原数减A^2的差乘100,只能上4，
1 . 4 ---------------------4就是B
-------------------
√2。00 00 00 00
1
----------------------------
24 )1 00 ---------------------24是20A+B,这个B是估的,要求A乘以20后加上B的和,
96 _____________96是B(20A+B)=4*24
----------------------------
4 00
这时,14(先不管小数点,这里小数点的位置不是重点)是A,此时的余数是400,14*20=280只能再上1,也就是B是1,这样(280+1)*1<400,并接近，到下一级
1 4 1
√2。00 00 00 00
1
---------------------------
24) 1 00
96
----------------------------
281 ) 4 00
2 81
----------------------------
1 19 00
同理此时A是141,余数是11900,1 19 00除以141*20，能上4，除数为2824,B为4,，到下一级
1 4 1 4
--------------------
√2。00 00 00 00
1
----------------------------
24 1 00
96
----------------------------
281 ) 4 00
2 81
----------------------------
2824 ) 1 19 00
1 12 96 _____B(20A+B)=4*(20*141+4)=11296
-----------------------------
6 04 00
同理
1 . 4 1 4 2
____________
√2。00 00 00 00
1
----------------------------
24) 1 00
96
----------------------------
281 ) 4 00
2 81
----------------------------
2824 ) 1 19 00
1 12 96
-----------------------------
28282 ) 6 04 00
5 65 64
----------------------------
38 36 00
自然对数e：
e=2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69995
95749 66967 62772 40766 30353 54759 45713 82178 52516 64274
27466 39193 20030 59921 81741 35966 29043 57290 03342 95260
59563 07381 32328 62794 34907 63233 82988 07531 95251 01901
15738 34187 93070 21540 89149 93488 41675 09244 76146 06680
82264 80016 84774 11853 74234 54424 37107 53907 77449 92069
55170 27618 38606 26133 13845 83000 75204 49338 26560 29760
67371 13200 70932 87091 27443 74704 72306 96977 20931 01416
92836 81902 55151 08657 46377 21112 52389 78442 50569 53696
77078 54499 69967 94686 44549 05987 93163 68892 30098 79312
77361 78215 42499 92295 76351 48220 82698 95193 66803 31825
28869 39849 64651 05820 93923 98294 88793 32036 25094 43117
30123 81970 68416 14039 70198 37679 32068 32823 76464 80429
53118 02328 78250 98194 55815 30175 67173 61332 06981 12509
96181 88159 30416 90351 59888 85193 45807 27386 67385 89422
87922 84998 92086 80582 57492 79610 48419 84443 63463 24496
84875 60233 62482 70419 78623 20900 21609 90235 30436 99418
49146 31409 34317 38143 64054 62531 52096 18369 08887 07016
76839 64243 78140 59271 45635 49061 30310 72085 10383 75051
01157 47704 17189 86106 87396 96552 12671 54688 95703 50354
.................
圆周率π
π=3.
1415926535 8979323846 2643383279 5028841971 6939937510
5820974944 5923078164 0628620899 8628034825 3421170679
8214808651 3282306647 0938446095 5058223172 5359408128
4811174502 8410270193 8521105559 6446229489 5493038196
4428810975 6659334461 2847564823 3786783165 2712019091
4564856692 3460348610 4543266482 1339360726 0249141273
7245870066 0631558817 4881520920 9628292540 9171536436
7892590360 0113305305 4882046652 1384146951 9415116094
3305727036 5759591953 0921861173 8193261179 3105118548
0744623799 6274956735 1885752724 8912279381 8301194912
9833673362 4406566430 8602139494 6395224737 1907021798
6094370277 0539217176 2931767523 8467481846 7669405132
0005681271 4526356082 7785771342 7577896091 7363717872
1468440901 2249534301 4654958537 1050792279 6892589235
4201995611 2129021960 8640344181 5981362977 4771309960
5187072113 4999999837 2978049951 0597317328 1609631859
5024459455 3469083026 4252230825 3344685035 2619311881
7101000313 7838752886 5875332083 8142061717 7669147303
5982534904 2875546873 1159562863 8823537875 9375195778
1857780532 1712268066 1300192787 6611195909 2164201989
3809525720 1065485863 2788659361 5338182796 8230301952
0353018529 6899577362 2599413891 2497217752 8347913151
5574857242 4541506959 5082953311 6861727855 8890750983
8175463746 4939319255 0604009277 0167113900 9848824012
8583616035 6370766010 4710181942 9555961989 4676783744
9448255379 7747268471 0404753464 6208046684 2590694912
9331367702 8989152104 7521620569 6602405803 8150193511
2533824300 3558764024 7496473263 9141992726 0426992279
6782354781 6360093417 2164121992 4586315030 2861829745
5570674983 8505494588 5869269956 9092721079 7509302955
3211653449 8720275596 0236480665 4991198818 3479775356
6369807426 5425278625 5181841757 4672890977 7727938000
8164706001 6145249192 1732172147 7235014144 1973568548
1613611573 5255213347 5741849468 4385233239 0739414333
4547762416 8625189835 6948556209 9219222184 2725502542
5688767179 0494601653 4668049886 2723279178 6085784383
8279679766 8145410095 3883786360 9506800642 2512520511
7392984896 0841284886 2694560424 1965285022 2106611863
0674427862 2039194945 0471237137 8696095636 4371917287
4677646575 7396241389 0865832645 9958133904 7802759009
9465764078 9512694683 9835259570 9825822620 5224894077
2671947826 8482601476 9909026401 3639443745 5305068203
4962524517 4939965143 1429809190 6592509372 2169646151
5709858387 4105978859 5977297549 8930161753 9284681382
6868386894 2774155991 8559252459 5395943104 9972524680
8459872736 4469584865 3836736222 6260991246 0805124388
4390451244 1365497627 8079771569 1435997700 1296160894
4169486855 5848406353 4220722258 2848864815 8456028506
0168427394 5226746767 8895252138 5225499546 6672782398
6456596116 3548862305 7745649803 5593634568 1743241125
1507606947 9451096596 0940252288 7971089314 5669136867
2287489405 6010150330 8617928680 9208747609 1782493858
9009714909 6759852613 6554978189 3129784821 6829989487
2265880485 7564014270 4775551323 7964145152 3746234364
5428584447 9526586782 1051141354 7357395231 1342716610
2135969536 2314429524 8493718711 0145765403 5902799344
0374200731 0578539062 1983874478 0847848968 3321445713
8687519435 0643021845 3191048481 0053706146 8067491927
8191197939 9520614196 6342875444 0643745123 7181921799
9839101591 9561814675 1426912397 4894090718 6494231961
5679452080 9514655022 5231603881 9301420937 6213785595
6638937787 0830390697 9207734672 2182562599 6615014215
0306803844 7734549202 6054146659 2520149744 2850732518
6660021324 3408819071 0486331734 6496514539 0579626856
1005508106 6587969981 6357473638 4052571459 1028970641
4011097120 6280439039 7595156771 5770042033 7869936007
数学辅导团为您解答
~
绛旓細鏈夊姛澶粰浣犳墦涓 鈭2鈮1.414 213562 鈭3鈮1.732 050808 鈭4=2 鈭5鈮2.236 067977 鈭6鈮2.449 489743 鈭7鈮2.645 751311 鈭8鈮2.828 427125 鈭9=3 鈭10鈮3.162 27766 鈭11鈮3.316 62479 鈭12鈮3.464 101615 鈭13鈮3.605 551275 鈭14鈮3.741 657387 鈭15鈮3....
绛旓細鏍瑰彿2鐨杩戜技鍊间负1.41421.鏍瑰彿鏄竴涓暟瀛︾鍙枫傛牴鍙锋槸鐢ㄦ潵琛ㄧず瀵逛竴涓暟鎴栦竴涓唬鏁板紡杩涜寮鏂硅繍绠鐨勭鍙枫傝嫢aⁿ=b锛岄偅涔坅鏄痓寮n娆℃柟鐨刵娆℃柟鏍规垨a鏄痓鐨1/n娆℃柟銆
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绛旓細鏍瑰彿2绾︾瓑浜1.414锛鏍瑰彿3绾︾瓑浜1.732锛屾牴鍙5绾︾瓑浜2.232锛屾牴鍙7绾︾瓑浜2.646銆傛牴寮忎箻闄ゆ硶娉曞垯锛1銆佸悓娆℃牴寮忕浉涔橈紙闄わ級锛屾妸鏍瑰紡鍓嶉潰鐨勭郴鏁扮浉涔橈紙闄わ級锛屼綔涓虹Н锛堝晢锛夌殑绯绘暟锛涙妸琚寮鏂鏁扮浉涔橈紙闄わ級锛屼綔涓鸿寮鏂规暟锛屾牴鎸囨暟涓嶅彉锛岀劧鍚庡啀鍖栨垚鏈绠鏍瑰紡銆2銆侀潪鍚屾鏍瑰紡鐩镐箻锛堥櫎锛夛紝搴斿厛鍖栨垚鍚屾鏍瑰紡鍚庯紝...
绛旓細鍏蜂綋鏂规硶...1锛2 .00 - 1 --- 2 4锛100 - 96 --- 281 锛400 2寮鏂寰1浣1 寰楁暟涔20鏀惧湪绗浜琛鏍瑰彿澶 浣欐暟琛ヤ袱涓0 100閲屾湁4涓20 鍙20涓24 寰楁暟1鐐瑰皬鏁扮偣鍚庝篃鍐4 鍒4*24=96 琚96鍑忕殑4 4琛ヤ袱涓0 14*20=280 鍐欏湪绗涓涓牴鍙峰 鍙280涓281 鐨勬暟涓婅竟1銆4鍚庤竟鍐1 銆傘
绛旓細2.骞虫柟鏍圭殑鐗规 骞虫柟鏍瑰叿鏈変互涓嬪嚑涓壒鎬э細闈炶礋鏁扮殑骞虫柟鏍规槸闈炶礋鏁般傞潪璐熸暟鐨勫钩鏂规牴瀛樺湪涓や釜鍊硷紝涓涓槸姝ｆ牴锛屽彟涓涓槸璐熸牴銆傝礋鏁扮殑骞虫柟鏍规槸澶嶆暟銆傛牴鍙风殑骞虫柟鍙互閫氳繃浠ヤ笅姝ラ鏉ヨ绠楋細灏嗘牴鍙蜂笅鐨勬暟杩涜寮鏂锛屽緱鍒颁竴涓笺傚皢杩欎釜鍊煎啀杩涜骞虫柟杩愮畻锛岀粨鏋滃氨鏄寮鏂圭殑鏁版湰韬3.濡備綍璁＄畻鏍瑰彿鐨勫钩鏂癸紵鏍瑰彿...
绛旓細鏍瑰彿2 (1.4+x)^2=2 1.96+2.8x鈮2 2.8x鈮0.04 x鈮0.014 鏍瑰彿2鈮1.414 鏍瑰彿3 1.7^2=22.89 (1.7+x)^2=3 2.89+3.4x鈮3 x鈮0.032 鏍瑰彿3鈮1.732 鏍瑰彿5 2.2^2=4.84 (2.2+x)^2=5 4.84+4.4x鈮5 x鈮0.036 鏍瑰彿5鈮2.236 鏍瑰彿6 2.4^2=5.76 (2.4+x)^...
绛旓細1.寮鏍瑰彿鐨勬柟娉曪細鍥犲紡鍒嗚В娉曘傚皢鏁板瓧鎹㈡垚骞虫柟鍜屾暟瀛楃殑涔樼Н寮鏍瑰彿銆2.涓句緥锛12=2脳2脳3=2鐨勫钩鏂姑3 锛 鈭12=鈭锛2鐨骞虫柟锛壝椻垰3=2鈭3锛8=2脳2脳2=2鐨勫钩鏂姑2锛屸垰8=鈭氾紙2鐨勫钩鏂癸級脳鈭2=2鈭2锛6=2脳3锛屾病鏈夊钩鏂癸紝鎵浠ヤ笉鑳藉紑鏍瑰彿锛18=3脳3脳2=3鐨勫钩鏂姑2锛屸垰18=鈭锛3鐨勫钩鏂癸級...
绛旓細绾︾瓑浜庢璐1.1892銆鏍瑰彿2鍗2鐨1/2娆℃柟锛岄偅涔堝啀瀵瑰叾鍙栧钩鏂规牴锛屾樉鐒跺嵆寰楀埌2鐨1/4娆℃柟鍜 -2鐨1/4娆℃柟锛屼娇鐢璁＄畻鍣ㄥ緱鍒扮害绛変簬姝ｈ礋1.1892銆傝〃绀轰负銆斅扁垰锟ｃ曪紝鍏朵腑灞炰簬闈炶礋鏁扮殑骞虫柟鏍圭О涔嬩负绠楁湳骞虫柟鏍广備竴涓鏁版湁涓や釜瀹炲钩鏂规牴锛屽畠浠簰涓虹浉鍙嶆暟锛岃礋鏁版湁涓や釜鍏辫江鐨勭函铏氬钩鏂规牴銆傚鏋滀竴涓潪璐熸暟x鐨...
绛旓細瑕佺煡閬撴庝箞寮骞虫柟鏍锛屼綘鍏堣娓呮鐨勭煡閬撳钩鏂规牴鐨勫叕寮忋1銆佸埄鐢ㄥ叕寮忓彲鐭ワ紝2鐨骞虫柟涔熷氨鏄2*2=4锛屾墍浠モ垰4 寮鏂鍚庡氨=2銆傚悓鐞嗗彲鐭モ垰9=3锛屸垰169=13 2銆佲垰2 寮鏂=1.414锛堜繚鐣欏皬鏁扮偣鍚涓浣嶏級銆傚彲浠ユ牴鎹璁＄畻鍥捐绠楀嚭鏉ャ
