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Rectangular root

Consider the VGA screen size of 640×480: these dimensions form a ratio of 4:3 and a product of 307,200 pixels. As a reciprocal of this, you could consider that the 4:3 rectangular roots of 307,200 are 640 and 480. A square root is then a rectangular root with a ratio of 1:1.

The challenge is to find an equation for solving rectangular roots. For example, what are the 4:3 rectangular roots of an image with one million pixels (one megapixel)? How do the answers compare to what you were expecting?

Solution to this one is courtesy of Jennifer Elaan.

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