Formula for Calculating Square RootsDate: 28 Jan 1995 13:11:21 -0500 From: Roger Gillies Subject: SQUARE ROOT Thanks for the information on exponent zero. Could you tell me: What is the formula for calculating square roots? R. Gillies Date: 28 Jan 1995 23:48:52 -0500 From: Dr. Ken Subject: Re: SQUARE ROOT Hello there! I found this description of a square-rooting algorithm in "Mathemagics" by Arthur Benjamin and Michael Brant Shermer. I'll copy it more or less verbatim, and we'll both learn, because I think I was about eight or nine years old the last time I saw this. 4. 3 5 8 Example: {19.00000000000 4^2 = 16 ----- 3 00 83 x 3 = 2 49 ------ 5100 865 x 5 = 4325 ------ 77500 8708 x 8 = 69664 Step 1: If the number of digits to the left of the decimal point is odd, then the first digit of the answer will be the largest number whose square is less than the first digit of the original number. If the number of digits to the left of the decimal point is even, then the first digit of the answer will be the largest number whose square is less than the first _two_ digits of the dividend. In this case, 19 is a 2-digit number, so the first digit of the quotient is the largest number whose square is less than 19, i.e. 4. Write that number above either the first digit of the dividend (if odd) or the second digit of the dividend (if even) Step 2: Subtract the square of the number in Step 1, then bring down two more digits. Step 3: Double the current quotient (on top, ignoring any decimal point), and put a blank space in front of it. Here 4 x 2 = 8. Put down 8_ x _ to the left of the current remainder, in this case 300. Step 4: The next digit of the quotient will be the largest number that can be put in both blanks so that the resulting multiplication problem is less than or equal to the current remainder. In this case, the number is 3, because 83 x 3 = 249, whereas 84 x 4 = 336 is too high. Write this number above the second digit of the next two numbers; in this case the 3 would go above the second 0. We now have a quotient of 4.3. Step 5: As long as you want more digits, subtract the product from the remainder (i.e. 300 - 249 = 51) and bring down the next two digits, in this case 51 turns into 5100, which becomes the current remainder. Now repeat steps 3 and 4. If you ever get a remainder of zero, you've got a perfect square on your hands. I hope this makes sense to you. -Ken "Dr." Math |
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