Approximations of reciprocal square roots are provided in IEEE floating point binary format by obtaining an index from an input value, accessing a pair of table values and performing a limited number of simple and rapidly performed manipulations. The maximum relative error in the approximation thus provided is less than 0.75/2(2k+1) as compared with a maximum relative error of 1/2k+2 of known methods, where 2k is the number of table entries.