diff --git a/src/libcore/num/f32.rs b/src/libcore/num/f32.rs
index b439f5577cbea..bf362928f61c3 100644
--- a/src/libcore/num/f32.rs
+++ b/src/libcore/num/f32.rs
@@ -259,7 +259,11 @@ impl Float for f32 {
 
     #[inline]
     fn sqrt(self) -> f32 {
-        unsafe { intrinsics::sqrtf32(self) }
+        if self < 0.0 {
+            NAN
+        } else {
+            unsafe { intrinsics::sqrtf32(self) }
+        }
     }
 
     #[inline]
diff --git a/src/libcore/num/f64.rs b/src/libcore/num/f64.rs
index d980009c0db0d..5ad2e2f9f8b59 100644
--- a/src/libcore/num/f64.rs
+++ b/src/libcore/num/f64.rs
@@ -266,7 +266,11 @@ impl Float for f64 {
 
     #[inline]
     fn sqrt(self) -> f64 {
-        unsafe { intrinsics::sqrtf64(self) }
+        if self < 0.0 {
+            NAN
+        } else {
+            unsafe { intrinsics::sqrtf64(self) }
+        }
     }
 
     #[inline]
@@ -377,4 +381,3 @@ impl Float for f64 {
         self * (value / 180.0)
     }
 }
-
diff --git a/src/libcore/num/mod.rs b/src/libcore/num/mod.rs
index 99d9d1df52220..42ea138acd4dc 100644
--- a/src/libcore/num/mod.rs
+++ b/src/libcore/num/mod.rs
@@ -1501,6 +1501,8 @@ pub trait Float: Signed + Primitive {
     fn frac_1_sqrt2() -> Self;
 
     /// Take the square root of a number.
+    ///
+    /// Returns NaN if `self` is not a non-negative number.
     fn sqrt(self) -> Self;
     /// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`.
     fn rsqrt(self) -> Self;
diff --git a/src/libstd/num/f32.rs b/src/libstd/num/f32.rs
index b2a9f1b7b20d3..f98e81bb2c878 100644
--- a/src/libstd/num/f32.rs
+++ b/src/libstd/num/f32.rs
@@ -787,4 +787,15 @@ mod tests {
         assert_eq!(NEG_INFINITY.integer_decode(), (8388608u64, 105i16, -1i8));
         assert_eq!(NAN.integer_decode(), (12582912u64, 105i16, 1i8));
     }
+
+    #[test]
+    fn test_sqrt_domain() {
+        assert!(NAN.sqrt().is_nan());
+        assert!(NEG_INFINITY.sqrt().is_nan());
+        assert!((-1.0f32).sqrt().is_nan());
+        assert_eq!((-0.0f32).sqrt(), -0.0);
+        assert_eq!(0.0f32.sqrt(), 0.0);
+        assert_eq!(1.0f32.sqrt(), 1.0);
+        assert_eq!(INFINITY.sqrt(), INFINITY);
+    }
 }
diff --git a/src/libstd/num/f64.rs b/src/libstd/num/f64.rs
index 6fe9fcad2aad7..5a5ca65a36de3 100644
--- a/src/libstd/num/f64.rs
+++ b/src/libstd/num/f64.rs
@@ -789,4 +789,15 @@ mod tests {
         assert_eq!(NEG_INFINITY.integer_decode(), (4503599627370496, 972, -1));
         assert_eq!(NAN.integer_decode(), (6755399441055744u64, 972i16, 1i8));
     }
+
+    #[test]
+    fn test_sqrt_domain() {
+        assert!(NAN.sqrt().is_nan());
+        assert!(NEG_INFINITY.sqrt().is_nan());
+        assert!((-1.0f64).sqrt().is_nan());
+        assert_eq!((-0.0f64).sqrt(), -0.0);
+        assert_eq!(0.0f64.sqrt(), 0.0);
+        assert_eq!(1.0f64.sqrt(), 1.0);
+        assert_eq!(INFINITY.sqrt(), INFINITY);
+    }
 }