This applet helps you understand the mental math method of estimating square roots that is taught in my posts at Grey Matters called Estimating Square Roots and Estimating Square Roots: Tips & Tricks. 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 never farther from the given number than .25. An online HTML5 version of this applet is available at: http://geogebratube.org/material/show/id/14587