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)

I'm not sure if I understand how this map is supposed to look like. If it maps \(x\) to \(x^2\), just take the square root. If it maps \(x\) to the smallest non-negative \(y\) such that \(x^2 \equiv y (\mod b) for some base \(b\), there is no inverse map because the function isn't injective.