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java中对于大数BigInteger,BigDecimal开根号没有提供函数，可以参考以下实现方法：

import java.math.BigDecimal;

import java.math.BigInteger;

public class BigSquareRoot {

final static BigInteger HUNDRED = BigInteger.valueOf(100);

public static BigDecimal sqrt(BigDecimal number, int scale, int roundingMode) {

e5a48de588b63231313335323631343130323136353331333337613139if (number.compareTo(BigDecimal.ZERO) < 0)

throw new ArithmeticException("sqrt with negative");

BigInteger integer = number.toBigInteger();

StringBuffer sb = new StringBuffer();

String strInt = integer.toString();

int lenInt = strInt.length();

if (lenInt % 2 != 0) {

strInt = '0' + strInt;

lenInt++;

}

BigInteger res = BigInteger.ZERO;

BigInteger rem = BigInteger.ZERO;

for (int i = 0; i < lenInt / 2; i++) {

res = res.multiply(BigInteger.TEN);

rem = rem.multiply(HUNDRED);

BigInteger temp = new BigInteger(strInt.substring(i * 2, i * 2 + 2));

rem = rem.add(temp);

BigInteger j = BigInteger.TEN;

while (j.compareTo(BigInteger.ZERO) > 0) {

j = j.subtract(BigInteger.ONE);

if (((res.add(j)).multiply(j)).compareTo(rem) <= 0) {

break;

}

}

res = res.add(j);

rem = rem.subtract(res.multiply(j));

res = res.add(j);

sb.append(j);

}

sb.append('.');

BigDecimal fraction = number.subtract(number.setScale(0, BigDecimal.ROUND_DOWN));

int fracLen = (fraction.scale() + 1) / 2;

fraction = fraction.movePointRight(fracLen * 2);

String strFrac = fraction.toPlainString();

for (int i = 0; i <= scale; i++) {

res = res.multiply(BigInteger.TEN);

rem = rem.multiply(HUNDRED);

if (i < fracLen) {

BigInteger temp = new BigInteger(strFrac.substring(i * 2, i * 2 + 2));

rem = rem.add(temp);

}

BigInteger j = BigInteger.TEN;

while (j.compareTo(BigInteger.ZERO) > 0) {

j = j.subtract(BigInteger.ONE);

if (((res.add(j)).multiply(j)).compareTo(rem) <= 0) {

break;

}

}

res = res.add(j);

rem = rem.subtract(res.multiply(j));

res = res.add(j);

sb.append(j);

}

return new BigDecimal(sb.toString()).setScale(scale, roundingMode);

}

public static BigDecimal sqrt(BigDecimal number, int scale) {

return sqrt(number, scale, BigDecimal.ROUND_HALF_UP);

}

public static BigDecimal sqrt(BigDecimal number) {

int scale = number.scale() * 2;

if (scale < 50)

scale = 50;

return sqrt(number, scale, BigDecimal.ROUND_HALF_UP);

}

public static void main(String args[]) {

BigDecimal num = new BigDecimal("6510354513.6564897413514568413");

long time = System.nanoTime();

BigDecimal root = sqrt(num, 1000);

time = System.nanoTime() - time;

System.out.println(root);

System.out.println(root.pow(2));

System.out.println(time);

}

}

执行结果：

80686.7678969512927493416316741557266722739984372151634715876752358049492663077817843059095146637911180490885758744651273281303288317374885332607051330176028572558172054217029042642080284121950891605518862273493239191320132148293688445347529243846517751025383884710742819252354014378344895438280908159584992112041354808433466321589387318739165992813377399669170549811704076258078653548749003251504791227309054913701062929858500433745971631998487835576600579373929233933246442803804132298016737159672317482520249763464713581048142915509001995943192415694815489364740152312416736301233269587910628885614893125235822493317184917626076223325819402403220531926392808333854523694780539563293133232729900988243013464020440976396084796739002581380094075169287492710301071487312491530290342213569053680461901907481289230152643599970138861788489599118674849815164425194138401918499233009571650761625943781367455101019720348741842171772915942278011905594031830367343193606047124373968951524359600676406162506362881367

6510354513.65648974135145684129999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999261018570188221952291201089398906052231483112444155137889353596770526763176032152876816872483428732651504536335267475372360148274382594285697529542224437785449440331424040251426099649509195223143651828659587364153208947136985285283628868915378240201094213227734756251495878566340409599684823659444904292099882985668906808623177208665251919370268937893457306121802766566270627041680526252368411023459487996551104603913903029501700835230597885867761183071537171958826568685086349210032834841075060512309444622145616551108119893623864579013813710941167261179972571233574705638862140357465569295994523261742960807593601727929262728856153880503561459736300910103299707873770713267018154171165545178430002342459940561678884530151166769964180453998734209554051691222326553700712948508454649608942746651683572634224323098274435576290709769148239120722342126902645574609770558211829972705514153006434846614016006956921594506606758832662240593485962629910320205678474047322232577044567479336985830934534290515788689

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