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Aperture is a purely geometrical property of an optical system. The term means either absolute aperture – the diameter of the objective lens, or, more generally, the diameter of the virtual image of the entry pupil (the white circle you see when you hold the objective lens up to the sky and look through the front).
The relative aperture (also called f-stop or focal ratio) is focal length of the objective divided by absolute aperture.
The multiplicative "square root of number of lenses" term makes no sense to me. It would mean the more lenses you have the bigger the aperture. That's clearly not the case. If anything, a larger number of lens elements reduces transmission.
Sometimes, esp. in photography, a corrective factor ("filter factor") is applied to the relative aperture, in order to account for filters or transmission losses (on a multitude of air-glass surfaces or in the glass itself).
However, no matter how much transmission is reduced, this only affects photographic exposure calculations and "overall brightness" of the visual image, but not aperture-related properties like Airy disc size, resolving power, etc.
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