This applet helps you understand the mental math method of estimating square roots that is taught in my posts at Grey Matters called [url=http://headinside.blogspot.com/2012/07/estimating-square-roots.html]Estimating Square Roots[/url] and [url=http://headinside.blogspot.com/2012/07/estimating-square-roots-tips-tricks.html]Estimating Square Roots: Tips & Tricks[/url].
Any number from 0 to 999 can be chosen with the sliders, and you can use the checkboxes to see display or hide the method used to determine the numerator and denominator.
This method gives a quick mental square root estimate whose square is [url=http://www.wolframalpha.com/input/?i=plot%5B%28%28%28floor%28sqrt%28x%29%29%29%2B%28%28x-%28%28floor%28sqrt%28x%29%29%29%5E2%29%29%2F%28%28%28floor%28sqr%28x%29%29%29*2%29%2B1%29%29%29%5E2%29-x*1.0%2C+%7Bx%2C+1%2C+1000%7D%5D]never farther from the given number than .25[/url].
An online HTML5 version of this applet is available at:
[url=http://geogebratube.org/material/show/id/14587]http://geogebratube.org/material/show/id/14587[/url]
