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From the wikipedia page on Gaussian blur.
Applying multiple, successive gaussian blurs to an image has the same effect as applying a single, larger gaussian blur, whose radius is the square root of the sum of the squares of the blur radii that were actually applied. For example, applying successive gaussian blurs with radii of 6 and 8 gives the same results as applying a single gaussian blur of radius 10, since sqrt {6^{2}+8^{2}}=10. Because of this relationship, processing time cannot be saved by simulating a gaussian blur with successive, smaller blurs — the time required will be at least as great as performing the single large blur.
