Floatingpointreciprocalsquarerootestimate (`frsqrte`) instructions are typically implemented as just such a table lookup, indexed by a few bits of the fraction and the LSB of the exponent.
The precision is typically limited to similar to bf16 (ARM, RISC-V) or fp16 (x86), so programs are expected to do a few Newton-Raphson iterations afterwards if they want more.