diff --git a/src/include/units/math.h b/src/include/units/math.h
new file mode 100644
index 00000000..377b1615
--- /dev/null
+++ b/src/include/units/math.h
@@ -0,0 +1,46 @@
+// The MIT License (MIT)
+//
+// Copyright (c) 2018 Mateusz Pusz
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#pragma once
+
+#include <units/quantity.h>
+#include <cmath>
+
+namespace std::experimental::units {
+
+  template<std::size_t N, typename U, typename Rep>
+  inline Quantity pow(const quantity<U, Rep>& q) noexcept
+  {
+    using dim = dimension_pow_t<typename U::dimension, N>;
+    using r = ratio_pow<typename U::ratio, N>;
+    return quantity<downcasting_traits_t<unit<dim, r>>, Rep>(std::pow(q.count(), N));
+  }
+
+  template<typename U, typename Rep>
+  inline Quantity sqrt(const quantity<U, Rep>& q) noexcept
+  {
+    using dim = dimension_sqrt_t<typename U::dimension>;
+    using r = ratio_sqrt<typename U::ratio>;
+    return quantity<downcasting_traits_t<unit<dim, r>>, Rep>(std::sqrt(q.count()));
+  }
+
+}  // namespace std::experimental::units
diff --git a/src/include/units/ratio.h b/src/include/units/ratio.h
index 157841f9..8a8a0a7f 100644
--- a/src/include/units/ratio.h
+++ b/src/include/units/ratio.h
@@ -118,6 +118,52 @@ namespace std::experimental::units {
   template<Ratio R1, Ratio R2>
   using ratio_divide = detail::ratio_divide_impl<R1, R2>::type;
 
+  // ratio_pow
+
+  namespace detail {
+
+    template<typename R, std::size_t N>
+    struct ratio_pow_impl {
+      using type = ratio_multiply<typename ratio_pow_impl<R, N - 1>::type, R>;
+    };
+
+    template<typename R>
+    struct ratio_pow_impl<R, 0> {
+      using type = R;
+    };
+
+  }
+
+  template<Ratio R, std::size_t N>
+  using ratio_pow = detail::ratio_pow_impl<R, N>::type;
+
+  // ratio_sqrt
+
+  namespace detail {
+
+    constexpr std::intmax_t sqrt_impl(std::intmax_t v, std::intmax_t l, std::intmax_t r)
+    {
+      if(l == r)
+        return r;
+
+      const auto mid = (r + l) / 2;
+      if(mid * mid >= v)
+        return sqrt_impl(v, l, mid);
+      else
+        return sqrt_impl(v, mid + 1, r);
+    }
+
+    static constexpr std::intmax_t sqrt_impl(std::intmax_t v)
+    {
+      return sqrt_impl(v, 1, v);
+    }
+
+  }
+
+  template<Ratio R>
+  using ratio_sqrt = ratio<detail::sqrt_impl(R::den), detail::sqrt_impl(R::num)>;
+
+
   // common_ratio
 
   namespace detail {
diff --git a/test/unit_test/test_custom_units.cpp b/test/unit_test/test_custom_units.cpp
index f8991953..0e5f5c79 100644
--- a/test/unit_test/test_custom_units.cpp
+++ b/test/unit_test/test_custom_units.cpp
@@ -22,7 +22,7 @@
 
 #include <units/dimensions/voltage.h>
 #include <units/dimensions/frequency.h>
-
+#include <units/math.h>
 
 /* ************** DERIVED DIMENSIONS THAT INCLUDE UNITS WITH SPECIAL NAMES **************** */
 
@@ -68,11 +68,11 @@ namespace {
   using namespace stde::units;
 
   // power spectral density
-  struct power_spectral_density : make_dimension_t<exp<voltage, 2>, exp<frequency, -1>> {};
+  struct power_spectral_density : make_dimension_t<units::exp<voltage, 2>, units::exp<frequency, -1>> {};
   struct sq_volt_per_hertz : unit<power_spectral_density> {};
 
   // amplitude spectral density
-  struct amplitude_spectral_density : make_dimension_t<exp<voltage, 1>, exp<frequency, -1, 2>> {};
+  struct amplitude_spectral_density : make_dimension_t<units::exp<voltage, 1>, units::exp<frequency, -1, 2>> {};
   // todo: add support for derived_unit
   //struct volt_per_sq_hertz : derived_unit<amplitude_spectral_density, kilogram, metre, second, ampere> {};
   struct volt_per_sqrt_hertz : unit<amplitude_spectral_density> {};
@@ -93,6 +93,7 @@ namespace {
   static_assert(std::is_same_v<dimension_sqrt_t<power_spectral_density>, amplitude_spectral_density>);
   static_assert(std::is_same_v<dimension_pow_t<amplitude_spectral_density, 2>, power_spectral_density>);
 
-  //static_assert(sqrt(quantity<sq_volt_per_hertz>(4)) = quantity<volt_per_sqrt_hertz>(2));
+  static_assert(std::is_same_v<decltype(pow<2>(quantity<volt_per_sqrt_hertz>(4))), decltype(quantity<sq_volt_per_hertz>(16))>);
+  static_assert(std::is_same_v<decltype(sqrt(quantity<sq_volt_per_hertz>(16))), decltype(quantity<volt_per_sqrt_hertz>(4))>);
 
 }