How to Compute Square Root of BigInteger in Java

In this example we will show how to find square root of BigInteger with NEWTON’s method.

Source Code

package com.beginner.examples;

import java.math.BigInteger;

public class FindSquareRootBigIntegerExample {

	public static void main(String[] args) {
		// 2 to the 1000
		BigInteger bigInteger = new BigInteger("2").pow(100);

		// Get its string
		String strBigNum = bigInteger.toString();

		if (strBigNum.length() % 2 == 1) {
			strBigNum = "0" + strBigNum;
		}

		// Store the remainder
		String remainder = "0";

		// Store the result
		String squareRootResult = "0";

		for (int i = 0; i < strBigNum.length() / 2; i++) {
			// The remainder plus the truncated two-digit number
			String remainder2 = remainder
					+ strBigNum.substring(i * 2, i * 2 + 2);

			BigInteger resultBigInteger = new BigInteger(squareRootResult);

			BigInteger remainderBigInteger = new BigInteger(remainder2);
			for (int j = 0; j <= 9; j++) {
				String num1 = "" + j;
				String num2 = "" + (j + 1);

				BigInteger testN1 = new BigInteger(num1);
				BigInteger testN2 = new BigInteger(num2);
				
				//Try,
				BigInteger n1_ = resultBigInteger
						.multiply(new BigInteger("20")).add(testN1);
				
				BigInteger n2_ = resultBigInteger
						.multiply(new BigInteger("20")).add(testN2);

				if (n1_.multiply(testN1).compareTo(remainderBigInteger)  0) {

					squareRootResult += j;

					remainder = remainderBigInteger.subtract(
							(n1_.multiply(testN1))).toString();

					break;
				}

			}

		}
		System.out.println(squareRootResult.substring(1));

	}

}

Output:

1125899906842624

References

Imported packages in Java documentation:

BigInteger