Pick a ratio and a second ratio to compound it with. The walkthrough simplifies first, then squares, roots, cubes, flips and merges, telling you at each step whether the result is a clean whole-number ratio or a surd.
Set the base to 4 : 9 to see the sub-duplicate come out clean at 2 : 3, and set the second ratio to 3 : 2 to watch a ratio compounded with its own inverse collapse to 1 : 1.