diff --git a/Arithmetic_kernel/include/CGAL/GMPXX_arithmetic_kernel.h b/Arithmetic_kernel/include/CGAL/GMPXX_arithmetic_kernel.h
new file mode 100644
index 00000000000..9c05981e0a6
--- /dev/null
+++ b/Arithmetic_kernel/include/CGAL/GMPXX_arithmetic_kernel.h
@@ -0,0 +1,44 @@
+// Copyright (c) 2016 Inria.
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; either version 3 of the License,
+// or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// Author: Marc Glisse <marc.glisse@inria.fr>
+
+#ifndef CGAL_GMPXX_ARITHMETIC_KERNEL_H
+#define CGAL_GMPXX_ARITHMETIC_KERNEL_H
+
+#include <CGAL/config.h>
+
+#ifdef CGAL_USE_GMPXX
+
+#include <CGAL/Arithmetic_kernel/Arithmetic_kernel_base.h>
+#include <CGAL/Get_arithmetic_kernel.h>
+
+#include <CGAL/gmpxx.h>
+
+namespace CGAL {
+/** \ingroup CGAL_Arithmetic_kernel
+ *  \brief The GMPXX set of exact number types
+ */
+struct GMPXX_arithmetic_kernel : internal::Arithmetic_kernel_base {
+  typedef mpz_class Integer;
+  typedef mpq_class Rational;
+};
+
+template <class T, class U>
+struct Get_arithmetic_kernel<__gmp_expr<T, U> > {
+  typedef GMPXX_arithmetic_kernel Arithmetic_kernel;
+};
+} //namespace CGAL
+#endif //CGAL_USE_GMPXX
+#endif
diff --git a/Arithmetic_kernel/test/Arithmetic_kernel/GMPXX_arithmetic_kernel.cpp b/Arithmetic_kernel/test/Arithmetic_kernel/GMPXX_arithmetic_kernel.cpp
new file mode 100644
index 00000000000..b51a5d6de00
--- /dev/null
+++ b/Arithmetic_kernel/test/Arithmetic_kernel/GMPXX_arithmetic_kernel.cpp
@@ -0,0 +1,18 @@
+#include <iostream>
+#include <CGAL/basic.h>
+#include <CGAL/GMPXX_arithmetic_kernel.h>
+
+#ifdef CGAL_USE_GMPXX
+
+#include <CGAL/Test/_test_arithmetic_kernel.h>
+
+int main() {
+  std::cout << "TEST GMPXX_arithmetic_kernel" << std::endl;
+  typedef CGAL::GMPXX_arithmetic_kernel AK;
+  CGAL::test_arithmetic_kernel<AK>();
+  return 0;
+}
+
+#else
+int main() { return 0; }
+#endif
diff --git a/Number_types/include/CGAL/Sqrt_extension/Sqrt_extension_type.h b/Number_types/include/CGAL/Sqrt_extension/Sqrt_extension_type.h
index b7290aec11e..e49109e2421 100644
--- a/Number_types/include/CGAL/Sqrt_extension/Sqrt_extension_type.h
+++ b/Number_types/include/CGAL/Sqrt_extension/Sqrt_extension_type.h
@@ -195,9 +195,10 @@ public:
     > >::type* = 0  )
   {
     typename Fraction_traits<NT>::Compose compose_nt;
+    typename Fraction_traits<ROOT>::Compose compose_root;
     if ( a != 0 ) {
       a0_ = compose_nt(-b,2*a);
-      root_ = CGAL_NTS square(a0_) - ROOT(c,a);
+      root_ = CGAL_NTS square(a0_) - compose_root(c,a);
       if(CGAL_NTS is_zero(root_)) {
 	is_extended_ = false;
       } else {
diff --git a/Number_types/include/CGAL/gmpxx.h b/Number_types/include/CGAL/gmpxx.h
index 5f65e85abff..429bf1b710e 100644
--- a/Number_types/include/CGAL/gmpxx.h
+++ b/Number_types/include/CGAL/gmpxx.h
@@ -61,4 +61,6 @@ class Real_embeddable_traits< ::__gmp_expr<T,U> >
 
 } //namespace CGAL
 
+#include <CGAL/GMPXX_arithmetic_kernel.h>
+
 #endif // CGAL_GMPXX_H
diff --git a/Number_types/test/Number_types/root_of_2.cpp b/Number_types/test/Number_types/root_of_2.cpp
index 32d6ac39be7..0b221b7d5e2 100644
--- a/Number_types/test/Number_types/root_of_2.cpp
+++ b/Number_types/test/Number_types/root_of_2.cpp
@@ -127,8 +127,8 @@ CGAL::Sqrt_extension<double,double,Tag1,Tag2> create_root_helper(RT a, RT b,CGAL
 template < class T, class RT,class Tag1, class Tag2 >
 CGAL::Sqrt_extension<T,T,Tag1,Tag2> create_root_helper(RT a, RT b, CGAL::Sqrt_extension<T,T,Tag1,Tag2> *)
 {
-  T t(a,b);
-  return CGAL::Sqrt_extension<T,T,Tag1,Tag2>( t );
+  typename CGAL::Fraction_traits<T>::Compose comp;
+  return CGAL::Sqrt_extension<T,T,Tag1,Tag2>( comp(a, b) );
 }
 
 template < class Root, class RT >
@@ -597,10 +597,8 @@ int main(int argc, char **argv) {
 #endif
 
 #ifdef CGAL_USE_GMPXX
-  std::cout << "Testing Sqrt_extension with Quotient mpz_class" << std::endl;
-  //no specialization of Get_arithmetic_kernel of mpz_class is available, the default is to suppose it is
-  //a ring type and make a field type using CGAL::Quotient.
-  result = result && test_root_of_g<CGAL::Sqrt_extension<CGAL::Quotient<mpz_class>,CGAL::Quotient<mpz_class>,CGAL::Tag_true,CGAL::Tag_true >,mpz_class,CGAL::Quotient<mpz_class> >();
+  std::cout << "Testing Sqrt_extension with mpq_class" << std::endl;
+  result = result && test_root_of<CGAL::Sqrt_extension<mpq_class,mpq_class,CGAL::Tag_true,CGAL::Tag_true > >();
 #endif
 
   if (result) {