using System;

using Extreme.Mathematics;

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string number = new string('1', 1998);

int digitIndex = 1000; // 1 based, not 0 based.  

​

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var num =  BigFloat.Parse(number);

var sqrt = BigFloat.Sqrt(num, AccuracyGoal.Absolute(digitIndex + 1), RoundingMode.TowardsNearest);

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var strSqrt = sqrt.ToString();

var decimalIndex = strSqrt.IndexOf('.');

var digit = strSqrt[decimalIndex + digitIndex]; // don't add +1 because digitIndex is already 1 based.

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Console.WriteLine($"The value of sqrt({(number.Length > 10 ? number.Substring(0, 10) + "..." : number)}) is {sqrt}.");

Console.WriteLine($"The {digitIndex} digit of sqrt({(number.Length > 10 ? number.Substring(0, 10) + "..." : number)}) is {digit}");