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)

>>7
23*23 = 529
123*123 = 15129
2123*2123 = 4507129
42123*42123 = 1774347129
142123*142123 = 20198947129
5142123*5142123 = 26441428947129
75142123*75142123 = 5646338648947129