diff --git a/constructible.py b/constructible.py
index 31b4188..1269854 100644
--- a/constructible.py
+++ b/constructible.py
@@ -178,6 +178,9 @@ class Constructible(object):
                                  self.a * other.b + self.b * other.a,
                                  self.field)
 
+        a, b = self.join(other)
+        return a * b
+
     def __truediv__(self, other):
         if not isinstance(other, Constructible):
             if isinstance(other, Rational):
@@ -239,18 +242,26 @@ class Constructible(object):
         if isinstance(other, Constructible) or isinstance(other, Rational):
             return (self -other)._sign() < 0
 
+        return NotImplemented
+
     def __gt__(self, other):
         if isinstance(other, Constructible) or isinstance(other, Rational):
             return (self -other)._sign() > 0
 
+        return NotImplemented
+
     def __le__(self, other):
         if isinstance(other, Constructible) or isinstance(other, Rational):
             return (self -other)._sign() <= 0
 
+        return NotImplemented
+
     def __ge__(self, other):
         if isinstance(other, Constructible) or isinstance(other, Rational):
             return (self -other)._sign() >= 0
 
+        return NotImplemented
+
     def join(self, other):
         '''return a tuple (new_self, new_other) such that
         new_self == self, new_other == other, and new_self.field == new_other.field '''

diff --git a/test_constructible.py b/test_constructible.py
index 13a43b6..5dadb24 100644
--- a/test_constructible.py
+++ b/test_constructible.py
@@ -239,6 +239,12 @@ class TestSqrt(TestCase):
         self.assertTrue(r > 0)
         self.assertEqual(r*r*r*r - 10*r*r + 1, 0)
 
+    def test_sqrt236(self):
+        from constructible import sqrt
+        r = sqrt(2) * sqrt(3)
+        self.assertTrue(r > 0)
+        self.assertEqual(r, sqrt(6))
+
     def test_sqrt235(self):
         from constructible import sqrt
         r = sqrt(2) + sqrt(3) + sqrt(5)

sqrt(2) * sqrt(3) returns None
```py
>>> print(sqrt(2) * sqrt(3))
None
>>> print(sqrt(2) / sqrt(3))
None
```

test_constructible.py::TestSqrt::test_sqrt236
test_constructible.py::TestHelperFunctions::test_fsqrt test_constructible.py::TestHelperFunctions::test_isqrt test_constructible.py::TestArithmeticOperators::test_expressions_type test_constructible.py::TestArithmeticOperators::test_mix_rational_binop test_constructible.py::TestArithmeticOperators::test_mix_rational_rbinop test_constructible.py::TestArithmeticOperators::test_rational_binop test_constructible.py::TestArithmeticOperators::test_rational_unop test_constructible.py::TestStrRepr::test_repr test_constructible.py::TestStrRepr::test_str test_constructible.py::TestComparison::test_comparison_Qsqrt2 test_constructible.py::TestComparison::test_rational_comparison test_constructible.py::TestSqrt::test_double_sqrt test_constructible.py::TestSqrt::test_sqrt23 test_constructible.py::TestSqrt::test_sqrt235 test_constructible.py::TestSqrt::test_sqrt_2 test_constructible.py::TestSqrt::test_sqrt_square test_constructible.py::TestTrySqrt::test_sqrt2