AArch64 NEON has the URSQRTE instruction, which gets closer to the OP's question than you might think; view a 32-bit value as a fixed-precision integer with 32 fractional bits (so the representable range is evenly spaced 0 through 1-ε, where ε=2^-32), then URSQRTE computes the approximate inverse square root, halves it, then clamps it to the range 0 through 1-ε. Fixed-precision integers aren't quite integers, and approximate inverse square root isn't quite square root, but it might get you somewhere close.
The related FRSQRTE instruction is much more conventional, operating on 32-bit floats, again giving approximate inverse square root.
The related FRSQRTE instruction is much more conventional, operating on 32-bit floats, again giving approximate inverse square root.