Square Root CalculationDate: 01/02/98 at 09:13:37 From: Robert Burdick Subject: Square root calculation I can't recall how we used to calculate the square root of a number before we learned to push a button on the calculator. One method, with paper and pencil. Another method, using calculator for a series of approximations. Date: 01/02/98 at 18:07:42 From: Doctor Jerry Subject: Re: square root calculation Hi Robert, The following can be used with either paper and pencil or calculator. Suppose that you wish to calculate the square root of a number A. The divide-and-average algorithm is: 1. Choose a rough approximation G of sqrt(A). 2. Divide A by G and then average the quotient with G, that is, calculate G* = ((A/G)+G)/2 3. If G* is sufficiently accurate, stop. Otherwise, let G = G* and return to step 2. Here's an example: To calculate the sqrt(2), choose G = 1.5. G* = (2/1.5 + 1.5)/2 = 1.41666666666 G* = (2/1.41666666666+1.41666666666)=1.41421568628 G* = (2/1.41421568628+1.41421568628)=1.41421356238 G* = (2/1.41421356238+1.41421356238)=1.41421356238 The number of correct decimal places more or less doubles with each repetition of step 2. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 01/03/98 at 15:43:21 From: Robert E. Burdick Subject: square root calculation Thanks for the solution. It works nicely. |
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