## October 21, 2008

**Geek entry of the day**

Another from the PG archives because I've got nuthin' today. As for those of you who think that that makes this day no different from any other, well, you have a point.

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Have you ever been caught off guard when someone walks up to you and asks, "What's the square root of *X*?" Me, too. Usually, I can remember approximations for most square roots up through, uh, maybe I won't finish that statement. Anyway, sometimes the numbers are just too damn big or I need more digits after the decimal place than I can comfortably work out. It's times like that when you really need Newton's formula:

*b* represents the number for which you're seeking the square root and *x* is your first guess. Wanna see how it all works? Of course you do! Observe:

Let's say that you need the square root of 13 and we want to be within 0.00001 of the actual value. For simplicity, we'll make *x* the same as *b*, the number we're taking the square root of.

Iterations

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x=13, b=13

NewX=7, difference is 6

x=7, b=13

NewX=4.428571, difference is 2.571429

x=4.428571,b=13

NewX=3.682028, difference is 0.746544

x=3.682028, b=13

NewX=3.606345, difference is 0.075682

x=3.606345, b=13

NewX=3.6055514, difference is 0.000794

x=3.6055514,b=13

NewX=3.605551, difference <0.000001

There you have it: the square root of 13 is approximately 3.605551.

Posted by: Physics Geek at
08:44 AM
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