diff --git a/BGL/examples/BGL_polyhedron_3/kruskal.cpp b/BGL/examples/BGL_polyhedron_3/kruskal.cpp
index f06179f34b2..1080b250cd4 100644
--- a/BGL/examples/BGL_polyhedron_3/kruskal.cpp
+++ b/BGL/examples/BGL_polyhedron_3/kruskal.cpp
@@ -42,7 +42,7 @@ kruskal(const Polyhedron& P)
   }
 
   
-  // We use the default edge weight which is the squared length of the edge
+  // We use the default edge weight which is the length of the edge
   // This property map is defined in graph_traits_Polyhedron_3.h
 
   // In the function call you can see a named parameter: vertex_index_map
diff --git a/BGL/examples/BGL_polyhedron_3/kruskal_with_stored_id.cpp b/BGL/examples/BGL_polyhedron_3/kruskal_with_stored_id.cpp
index 85207e466ca..5d811882822 100644
--- a/BGL/examples/BGL_polyhedron_3/kruskal_with_stored_id.cpp
+++ b/BGL/examples/BGL_polyhedron_3/kruskal_with_stored_id.cpp
@@ -23,7 +23,7 @@ void
 kruskal( const Polyhedron& P)
 {
 
-  // We use the default edge weight which is the squared length of the edge
+  // We use the default edge weight which is the length of the edge
   // This property map is defined in graph_traits_Polyhedron_3.h
   
   // This function call requires a vertex_index_map named parameter which
diff --git a/BGL/include/CGAL/boost/graph/graph_traits_Delaunay_triangulation_2.h b/BGL/include/CGAL/boost/graph/graph_traits_Delaunay_triangulation_2.h
index 98ec63d738c..8b36e09112a 100644
--- a/BGL/include/CGAL/boost/graph/graph_traits_Delaunay_triangulation_2.h
+++ b/BGL/include/CGAL/boost/graph/graph_traits_Delaunay_triangulation_2.h
@@ -273,7 +273,7 @@ namespace CGAL {
     { }
 
     typename Gt::FT operator[](key_type e) const {
-      return tr.segment(e).squared_length();
+      return approximate_sqrt(tr.segment(e).squared_length());
     }
   };
 
diff --git a/BGL/include/CGAL/boost/graph/graph_traits_Triangulation_2.h b/BGL/include/CGAL/boost/graph/graph_traits_Triangulation_2.h
index 695d15d1494..6d5d426bbf0 100644
--- a/BGL/include/CGAL/boost/graph/graph_traits_Triangulation_2.h
+++ b/BGL/include/CGAL/boost/graph/graph_traits_Triangulation_2.h
@@ -695,7 +695,7 @@ namespace CGAL {
     { }
 
     value_type operator[](key_type e) const {
-      return tr.segment(e).squared_length();
+      return approximate_sqrt(tr.segment(e).squared_length());
     }
   };
 
diff --git a/BGL/include/CGAL/boost/graph/properties_CombinatorialMap.h b/BGL/include/CGAL/boost/graph/properties_CombinatorialMap.h
index ba6259ee7be..30daae2c0e3 100644
--- a/BGL/include/CGAL/boost/graph/properties_CombinatorialMap.h
+++ b/BGL/include/CGAL/boost/graph/properties_CombinatorialMap.h
@@ -22,6 +22,7 @@
 #include <CGAL/boost/graph/properties.h>
 #include <CGAL/Unique_hash_map.h>
 #include <CGAL/Linear_cell_complex.h>
+#include <CGAL/number_utils.h>
 
 #define CGAL_LCC_ARGS unsigned int d_, unsigned int ambient_dim, \
              class Traits_, \
@@ -37,18 +38,20 @@ namespace CGAL {
 template<class LCC>
 class LCC_edge_weight_map : public boost::put_get_helper<double, LCC>
 { 
+  typedef typename LCC::Point Point;
+  typedef typename Kernel_traits<Point>::Kernel::FT FT;
 public:
 
-  typedef boost::readable_property_map_tag                                category;
-  typedef double                                                          value_type;
-  typedef double                                                          reference;
+  typedef boost::readable_property_map_tag                         category;
+  typedef FT                                                       value_type;
+  typedef FT                                                       reference;
   typedef typename boost::graph_traits<LCC const>::edge_descriptor key_type;
 
   LCC_edge_weight_map(LCC const& ) {}
 
   reference operator[](key_type const& e) const
   {
-    return CGAL::squared_distance(LCC::point(e), LCC::point(e->opposite()));
+    return approximate_sqrt(CGAL::squared_distance(LCC::point(e), LCC::point(e->opposite())));
   }
 };
 
diff --git a/BGL/include/CGAL/boost/graph/properties_Polyhedron_3.h b/BGL/include/CGAL/boost/graph/properties_Polyhedron_3.h
index 7db008288df..af3fdc49c32 100644
--- a/BGL/include/CGAL/boost/graph/properties_Polyhedron_3.h
+++ b/BGL/include/CGAL/boost/graph/properties_Polyhedron_3.h
@@ -24,6 +24,7 @@
 #include <CGAL/boost/graph/graph_traits_Polyhedron_3.h>
 #include <CGAL/Unique_hash_map.h>
 #include <CGAL/squared_distance_2_1.h>
+#include <CGAL/number_utils.h>
 #include <boost/shared_ptr.hpp>
 
 #define CGAL_HDS_PARAM_ template < class Traits, class Items, class Alloc> class HDS
@@ -84,23 +85,19 @@ private:
   boost::shared_ptr<Map> map_;
 };
 
-template<typename Handle>
+  template<typename Handle, typename FT>
 struct Wrap_squared
-  : boost::put_get_helper< double, Wrap_squared<Handle> >
+    : boost::put_get_helper< double, Wrap_squared<Handle,FT> >
 {
-  typedef double value_type;
-  typedef double reference;
+  typedef FT value_type;
+  typedef FT reference;
   typedef Handle key_type;
   typedef boost::readable_property_map_tag category;
 
   template<typename E>
-  double
-  // TODO Kernel::FT, this is as bad as the old code, we need to
-  // forward the halfedge type in HDS_edge to extract the kernel here.
-  // Technically, there is also a general implementation for
-  // HalfedgeGraph to prevent duplication in Surface_mesh.
+  FT
   operator[](const E& e) const {
-    return CGAL::squared_distance(e.halfedge()->vertex()->point(), e.halfedge()->opposite()->vertex()->point());
+    return approximate_sqrt(CGAL::squared_distance(e.halfedge()->vertex()->point(), e.halfedge()->opposite()->vertex()->point()));
   }
 };
 
@@ -229,10 +226,9 @@ struct Polyhedron_property_map<boost::edge_weight_t>
   template<class Gt, class I, CGAL_HDS_PARAM_, class A>
   struct bind_
   {
-    typedef internal::Wrap_squared<
-      typename boost::graph_traits<
-        CGAL::Polyhedron_3<Gt, I, HDS, A>
-        >::edge_descriptor > type;
+    typedef typename CGAL::Polyhedron_3<Gt, I, HDS, A>::Traits::FT FT;
+    typedef typename boost::graph_traits<CGAL::Polyhedron_3<Gt, I, HDS, A> >::edge_descriptor edge_descriptor;
+    typedef internal::Wrap_squared<edge_descriptor,FT> type;
     typedef type const_type;
   };
 };
diff --git a/BGL/include/CGAL/boost/graph/properties_Surface_mesh.h b/BGL/include/CGAL/boost/graph/properties_Surface_mesh.h
index 1da0fc360e3..cf91c647c8c 100644
--- a/BGL/include/CGAL/boost/graph/properties_Surface_mesh.h
+++ b/BGL/include/CGAL/boost/graph/properties_Surface_mesh.h
@@ -25,6 +25,7 @@
 #include <CGAL/Surface_mesh.h>
 #include <CGAL/Kernel_traits.h>
 #include <CGAL/squared_distance_3.h>
+#include <CGAL/number_utils.h>
 
 #include <CGAL/boost/graph/properties.h>
 
@@ -52,8 +53,8 @@ public:
 
   value_type operator[](const key_type& e) const
   {
-    return CGAL::sqrt(CGAL::squared_distance(pm_[source(e, sm_)],
-                                             pm_[target(e, sm_)]));
+    return approximate_sqrt(CGAL::squared_distance(pm_[source(e, sm_)],
+                                                   pm_[target(e, sm_)]));
   }
 
 private: