Square Roots Without a Calculator
Date: 8/6/96 at 17:11:52 From: sjump16 Subject: Square Roots Without a Calculator How do you get a square root without a calculator? What is the square root of 7 to 5 decimal places? Thanks. Steve Davis
Date: 8/6/96 at 21:26:54 From: Doctor Robert Subject: Re: Square Roots Without a Calculator In order to do this, you have to learn a square root algorithm. Get out a piece of paper and a pencil. I hope that I can explain it well enough just using words. First, write down the decimal 7.00000000 and mark off pairs of digits starting from the decimal point. This gives you 7.00'00'00'00'... To start, guess at the square root of 7. The nearest integer(without going over) is 2. Now set the thing up like a long division. 2 divides into 7 2 times. 2 x 2 = 4. Subtract that from 7 which leaves 3 and bring down the next two digits. Now comes the part that's different from division. The answer showing so far is 2. Double that and use the 4 as the first digit of a new divisor. Whatever goes in the one's place must also go up in the answer. In other words, the question is: forty something goes into 300 how many times?. The answer is 6. Forty-six times six = 276. Subtract that from 300 leaving 24. Bring down the next two zeros. Double what's in the answer (double 26). Use 52 as the first two digits in a new divisor and the question becomes five hundred and twenty something divides into twenty-four hundred how many times? The answer is 4. 4 times 524 = 2096. Subtract from 2400. Bring down two more zeros. Double the answer and leave an empty digit and so on and so forth. You can keep going forever. So now, you know you are smarter than a calculator! Once you see how this goes, it's not that hard. If you want a hard one, try the algorithm for finding a cube root (I don't know it). Hope that you can follow this. -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.