diff --git a/bls12_381/src/fields/tests.rs b/bls12_381/src/fields/tests.rs
index d242915..7b667af 100644
--- a/bls12_381/src/fields/tests.rs
+++ b/bls12_381/src/fields/tests.rs
@@ -1117,6 +1117,19 @@ fn test_fq_repr_add_nocarry() {
     assert!(x.is_zero());
 }
 
+#[test]
+fn test_fq2_sqrt() {
+    // 1 has a sqrt in the base field
+    let fq2_sqrt = Fq2::new(Fq::one(), Fq::zero()).sqrt().unwrap();
+    assert_eq!(fq2_sqrt.c0, Fq::one());
+    assert_eq!(fq2_sqrt.c1, Fq::zero());
+
+    // -1 has no sqrt in the base field, but should be valid in Fq2
+    let fq2_sqrt = Fq2::new(-Fq::one(), Fq::zero()).sqrt().unwrap();
+    assert_eq!(fq2_sqrt.c0, Fq::zero());
+    assert_eq!(fq2_sqrt.c1, Fq::one());
+}
+
 #[test]
 fn test_fq_num_bits() {
     assert_eq!(FqParameters::MODULUS_BITS, 381);