Find an exact square root bound
Enter a nonnegative whole number to find the largest integer r whose square is at most your number. The result includes r squared, the remainder, the next square, and a perfect-square check. For 27, the floor root is 5 and the remainder is 2.
How it works
Integer Newton iteration finds the root using exact BigInt arithmetic. The remainder is n − r². A zero remainder means the input is a perfect square; otherwise the true square root lies strictly between r and r + 1.
Input and privacy
Enter 0 or a positive integer with up to 1000 digits. Decimals, signs, separators, and scientific notation are not accepted. Results remain exact even beyond JavaScript's normal safe integer range. All calculations run locally in your browser.