diff --git a/Number_types/include/CGAL/MP_Float.h b/Number_types/include/CGAL/MP_Float.h
index ee2bca7a564..53d7d00aa94 100644
--- a/Number_types/include/CGAL/MP_Float.h
+++ b/Number_types/include/CGAL/MP_Float.h
@@ -404,6 +404,14 @@ to_double(const Root_of_2<MP_Float> &r)
 {
   const MP_Float &ra = r[2];
   const MP_Float &rb = r[1];
+
+  if(r.is_rational()) {
+    std::pair<double, int> n = to_double_exp(rb);
+    std::pair<double, int> d = to_double_exp(ra);
+    double scale = CGAL_CLIB_STD::ldexp(1.0, n.second - d.second);
+    return (n.first / d.first) * scale;
+  }
+
   const MP_Float &rc = r[0];
 
   std::pair<double, int> pa = to_double_exp(ra);
@@ -431,6 +439,14 @@ to_interval(const Root_of_2<MP_Float> &r)
 
   const MP_Float &ra = r[2];
   const MP_Float &rb = r[1];
+
+  if(r.is_rational()) {
+    std::pair<std::pair<double, double>, int> n = to_interval_exp(rb);
+    std::pair<std::pair<double, double>, int> d = to_interval_exp(ra);
+    return ldexp(Interval_nt<>(n.first) / Interval_nt<>(d.first),
+               n.second - d.second).pair();
+  }
+
   const MP_Float &rc = r[0];
 
   if(is_zero(rc)) {
@@ -440,14 +456,14 @@ to_interval(const Root_of_2<MP_Float> &r)
       std::pair<std::pair<double, double>, int> pb = to_interval_exp(rb);
       Interval_nt<> a = ldexp(Interval_nt<>(pa.first),pa.second);
       Interval_nt<> b = ldexp(Interval_nt<>(pb.first),pb.second);  
-      return (CGAL::sqrt(-b/a)).pair();
+      return (-b/a).pair();
     } 
     if(r.is_smaller()) {
       std::pair<std::pair<double, double>, int> pa = to_interval_exp(ra);
       std::pair<std::pair<double, double>, int> pb = to_interval_exp(rb);
       Interval_nt<> a = ldexp(Interval_nt<>(pa.first),pa.second);
       Interval_nt<> b = ldexp(Interval_nt<>(pb.first),pb.second);  
-      return (CGAL::sqrt(-b/a)).pair();
+      return (-b/a).pair();
     } return std::make_pair(0.0,0.0);
   }