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You can do:

sage: a = sqrt(6) * sqrt(3) * sqrt(2)
sage: a.canonicalize_radical()
6

canonicalize_radical is not parrt of the full_simplify method, IIRC because of some monodromy issues (winding around singularities in the complex plane does not commute with chosing a single square root), canonicalize_radical is not parrt of the full_simplify method anymore.

You can do:

sage: a = sqrt(6) * sqrt(3) * sqrt(2)
sage: a.canonicalize_radical()
6

canonicalize_radical is not parrt of the full_simplify method, IIRC because of some monodromy issues (winding around singularities in the complex plane does not commute with chosing a single square root), canonicalize_radical is not parrt of the full_simplify method anymore.

You can do:

sage: a = sqrt(6) * sqrt(3) * sqrt(2)
sage: a.canonicalize_radical()
6

canonicalize_radical is not parrt of the full_simplify method, IIRC because of some monodromy issues (winding around singularities in the complex plane does not commute with chosing a single square root), branch of a multi-valued function), canonicalize_radical is not parrt of the full_simplify method anymore.

Here, since everything is assumed to be real, there is no real issue.