Karatsuba Square Root

We exhibit an algorithm to compute the square-root with remainder of a n-word number in 3\2word operations, where K(n) is the number of words operations to multiply two n-word numbers using Karatsuba's algorithm. If the remainder is not needed, the cost can be reduced to K(n) on average. This algorithm can be used for floating-point or polynomial computations too; although not optimal asymptotically, its simplicity gives a wide range of use, from about 50 to 1,000,000 digits, as shown by computer experiments.