Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site exodus.UUCP Path: utzoo!watmath!clyde!burl!ulysses!gamma!exodus!rwh From: rwh@exodus.UUCP (Roy Haas) Newsgroups: net.math Subject: Re: Square Roots give Powers Message-ID: <221@exodus.UUCP> Date: Fri, 21-Sep-84 09:39:45 EDT Article-I.D.: exodus.221 Posted: Fri Sep 21 09:39:45 1984 Date-Received: Tue, 25-Sep-84 20:49:57 EDT References: <9092@watmath.UUCP> Organization: Bell Communications Research, Inc., Murray Hill, NJ Lines: 13 Since the limit lim [ y( x^(1/2n) + 1 ]^2n = x^y n-> inf holds (use L'Hospital's Rule), your algorithm works for "large n". The rate of convergence depends on how large x is, since repeated rooting drives x^1/2n to 1. It also depends on how large y is, since y(x^1/2n - 1) must approach 0. Note that the algorithm is only useful as an approximatiion for y where the fractional part has an infinite binary expansion (otherwise you can compute x^y exactly in a finite number of steps).