Cube rootsDate: 05/30/97 at 09:34:01 From: Elena Subject: Cube roots Dear Dr. Math, How can I can figure out the cube root of a number? (i.e., that the cube root of 216 is 6). Thank you for helping me! Elena Date: 05/31/97 at 08:30:28 From: Doctor Jerry Subject: Re: Cube roots Hi Elena, There isn't a "test" that you can apply to an integer to determine whether it is a cube of an integer, other than looking it up in a table. Perhaps you are asking for an algorithm to calculate the cube root of any positive number. If a is the number you want the cube root of, make a guess and call it g. The next guess is G = (2/3)*g + (1/3)*(a/(g^2)). Repeat this until the cube root is found to desired accuracy. If a = 8, for example, suppose our first guess is 3. Using the above formula, here are the successive guesses: g1 = 3 g2 = 2.2962962963 g3 = 2.03658740252 g4 = 2.00065335855 g5 = 2.00000021335 g6 = 2.00000000000 ( to the accuracy of my calculator) -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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