public class SquareRoot {
	public static double sqrt(double num) {
		double errorAllowed = 0.00000001;
		double lowBound = 1;
		double highBound = num;
		double result = (lowBound + highBound) / 2;
		while (result * result - num > errorAllowed || num - result * result > errorAllowed) {
			if(result * result - num > errorAllowed) {
				highBound = result;
			} else {
				lowBound = result;
			}
			result = (lowBound + highBound) / 2;
		}
		return result;
	}

	public static void main(String[] args) {
		System.out.println(sqrt(2));
	}
}