Methods and apparatus for determining a unique audience exposed to media while reducing memory resources of a computing device are disclosed herein. An example method includes receiving impression requests at a server from a plurality of client devices via a network; based on the impression requests, logging, with the server, a plurality of impressions corresponding to the media accessed at the client devices; obtaining a number of demographic impressions logged by a database proprietor; obtaining a number of registered users of the database proprietor exposed to the media; multiplying, by executing an instruction with a processor, a number of the plurality of impressions by a square of the number of the registered users to generate a product; dividing, by executing an instruction with the processor, the product by a number of the demographic impressions to generate a quotient; and determining, by executing an instruction with the processor, the unique audience based on a square root of the quotient.