I just put up a new post with a simple method for estimating square roots of ANY number from 1 to 1,000:
http://headinside.blogspot.com/2012/07/e......ots.html

With this method, you can quickly determine the approximate square root of any whole number from 1 to 1,000, and you'll never be off the requested number by more than .25! For example, if you're given the number 157, this method will show you how to come up with the root of 12 and 13/25ths as the root. When squared, that comes to 156.7504 - less than .25 off of 157!

You do have to know the perfect squares of every number from 1 to 31, but if you know that, you're more than halfway there.

I developed this method on my own through experimentation, but it's so simple and straightforward, I can't imagine I'm the originator. Yet, I haven't been able to find any reference to this approach. If anyone knows where I can find out more about this approach, I'd appreciate a reference.

As one commenter has already put it, once you practice this method, the square roots almost "fall out of your mind".

Nice and easy Scott. Thanks.

You're welcome, landmark.

In today's post, I add some tips and tricks to help make this more theatrical:
http://headinside.blogspot.com/2012/07/e......cks.html

To make the method easier to visualize, I created this web app. Use the sliders to change the given number (anywhere from 0 to 999), and click the checkboxes to see how the numerator and denominator are worked out.



I happened to run across a similar method, although mine works out to be a little more accurate:
http://homeschoolmath.blogspot.com/2009/......tal.html