Square root calculator

Every digit comes from the digit-by-digit long division method over BigInt, the same pencil recurrence taught in school: bring down a pair, find the largest d with (20p + d) × d that fits, write d. That makes the root exact at any precision in range, including 50 decimal places. Radical simplification factors the radicand by trial division and is capped at 10^12, where the cap is disclosed rather than guessed past; the root stays exact either way.