Fast integer inverse root mapping

This came up in a /sci thread
(1-10 ->)
1,4,9,(1)6,(2)5,(3)6,(4)9,(6)4,(8)1,(10)0

How difficult is reverse mapping a square this way? (it runs least significant digit first lol)

>>2
It should map \(x\) to \(x^2\), ie perform an integer square root, but it only keeps the 1-10 lookup table, and has a two:one branch per digit