correct parent for square root of constant polynomial

src/sage/rings/laurent_series_ring_element.pyx

@@ -751,6 +751,14 @@ cdef class LaurentSeries(AlgebraElement):
             t^-3 + t^3 + O(t^9)
 
         ALGORITHM: Shift the unit parts to align them, then add.
+
+        TESTS:
+
+        Verify that :trac:`35860` is fixed::
+
+            sage: R.<t> = LaurentPolynomialRing(ZZ)
+            sage: sqrt(t^2) + t^-1
+            t^-1 + t
         """
         cdef LaurentSeries right = <LaurentSeries>right_m
         cdef long m

src/sage/rings/polynomial/polynomial_element.pyx

@@ -1988,6 +1988,12 @@ cdef class Polynomial(CommutativePolynomial):
             False
             sage: R(0).is_square()
             True
+
+        Make sure :trac:`35860` is fixed::
+
+            sage: S.<x> = PolynomialRing(ZZ)
+            sage: is_square(S(1), True)[1].parent()
+            Univariate Polynomial Ring in x over Integer Ring
         """
         if self.is_zero():
             return (True, self) if root else True
@@ -2000,7 +2006,7 @@ cdef class Polynomial(CommutativePolynomial):
         u = self._parent.base_ring()(f.unit())
 
         if all(a[1] % 2 == 0 for a in f) and u.is_square():
-            g = u.sqrt()
+            g = self._parent(u.sqrt())
             for a in f:
                 g *= a[0] ** (a[1] // 2)
             return (True, g) if root else True