Square Roots: Guess, Divide, Average
Date: 6/23/96 at 12:10:58 From: Anonymous Subject: Square Roots What is the formula for square roots?
Date: 6/24/96 at 10:45:59 From: Doctor Ethan Subject: Re: Square Roots I am not sure what you mean by the "formula for square roots." I am going to assume that you want a formula for finding the square root of a number and I am afraid that no such formula exists. There are methods you can use to approximate the square root. I will teach you my favorite. Remember, the square root of a number is just the number which when multiplied by itself gives the first number. So 2 is the square root of 4 because 2 * 2 = 4. Now here is the method: Start with the number you want to find the square root of. Let's use 12. There are three steps: 1. Guess 2. Divide 3. Average. Then you just keep repeating steps 2 and 3. So let's do it. First, start by guessing a square root value. It helps if your guess is a good one but it will work even if it is a terrible guess. Just to show you that I will guess that 2 is the square root of 12. Now in step two, I divide 12 by my guess of 2 and I get 6. Now in step three, I average 6 and 2: (6+2)/2 = 4 Now I repeat step two with the new guess of 4. So 12/4 = 3 Now average 4 and 3: (4+3)/2 = 3.5 Now repeat step two: 12/3.5 = 3.43 Now average: (3.5 + 3.43)/2 = 3.465 We could keep going forever, getting a better and better approximation but let's stop here to see how we are doing. 3.465 * 3.465 = 12.006225 That is pretty close to 12, so we are doing pretty well. Hope that this helps you. -Doctor Ethan, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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