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Square Roots (College Algebra's Blog)

College-Cram.com:: College Algebra:: Square Roots (College Algebra's Blog)

August 09, 2007

Dear Professor Cram:

First I must tell you, that I am so happy to have found your site, it has given me hope that I can learn what I need to advance in my college studies. Here is my question: how do you find the square root of a radicand?

D. B., University of Louisiana

Thank you for your feedback, we love to hear from people we are helping.

To answer your question, there are several ways of finding a square root. The easiest is to use a calculator -- just enter the radicand, press the square root key, and *bam* there's your answer. Barring a calculator, there is a long, drawn-out method for calculating square roots that looks a bit like long division and hasn't been taught in schools in a long, long time.

For a quick and dirty approximate answer, the Babylonian Method is your best bet. Basically, you guess at the answer (let's call your guess 'A'.) Divide your radicand by 'A' and average that with 'A', with that answer being your new 'A'. Repeat until you get the same answer two times in a row.

For example, say you're looking for the square root of 69. We'll guess 8. Do the averaging (I'm only going to 3 decimal places):

  • 69/8 = 8.625
  • A = (8 + 8.625)/2, or 8.313

Now repeat, with 8.313 as the new guess:

  • 69/8.313 = 8.300
  • A = (8.313 + 8.300)/2, or 8.307

And again, with 8.307 as the new guess:

  • 69/8.307 = 8.306
  • A = (8.307 + 8.306)/2, or 8.307

We got 8.307; if you use your calculator, you'll see that the square root of 69 is in fact 8.3066238629180748525842627449075. Not too far off, those Babylonians.

Good Studying,

Professor Cram

Posted by Professor Cram @ College Algebra

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