diff --git a/README.md b/README.md
@@ -133,6 +133,8 @@ CHANGELOG
 
 Next release:
 
+- [gh-172](https://github.com/flintlib/python-flint/pull/161)
+  Add `fmpz_is_square`.
 - [gh-161](https://github.com/flintlib/python-flint/pull/161)
   Add `acb.lerch_phi` to compute the Lerch transcendent.
 - [gh-132](https://github.com/flintlib/python-flint/pull/132)
@@ -146,7 +148,7 @@ Next release:
 - [gh-148](https://github.com/flintlib/python-flint/pull/148)
   Remove debug symbols to make smaller Linux binaries.
 - [gh-144](https://github.com/flintlib/python-flint/pull/144)
-  Add `rel_one_ccuracy_bits` to `arb` and `acb`.
+  Add `rel_one_accuracy_bits` to `arb` and `acb`.
 - [gh-142](https://github.com/flintlib/python-flint/pull/142)
   Add `acb_theta` module for the numerical evaluation of [theta
   functions](https://flintlib.org/doc/acb_theta.html) (only available for

diff --git a/src/flint/test/test_all.py b/src/flint/test/test_all.py
@@ -294,6 +294,8 @@ def test_fmpz_functions():
             [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0]),
         (lambda n: flint.fmpz(n).is_perfect_power(),
             [T, T, T, F, F, T, F, F, F, T, T, F]),
+        (lambda n: flint.fmpz(n).is_square(),
+            [F, T, T, F, F, T, F, F, F, F, T, F]),
         (lambda n: flint.fmpz(n).partitions_p(),
             [0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42]),
         (lambda n: flint.fmpz(n).moebius_mu(),

diff --git a/src/flint/types/fmpz.pyx b/src/flint/types/fmpz.pyx
@@ -683,11 +683,31 @@ cdef class fmpz(flint_scalar):
         return fmpz_is_probabprime(self.val)
 
     def is_perfect_power(self):
+        r"""
+        Return True if this integer is of the form `r^k` with `k>1`, False otherwise.
+        `0, 1, -1` are considered perfect powers.
+
+            >>> fmpz(81).is_perfect_power()
+            True
+            >>> fmpz(1234).is_perfect_power()
+            False
+        """
         cdef int k
         cdef fmpz v = fmpz()
         k = fmpz_is_perfect_power(v.val, self.val)
         return k != 0
 
+    def is_square(self):
+        r"""
+        Return True if perfect square and False otherwise.
+
+            >>> fmpz(25).is_square()
+            True
+            >>> fmpz(101).is_square()
+            False
+        """
+        return fmpz_is_square(self.val) != 0
+
     def partitions_p(n):
         r"""
         Returns `p(n)`, the number of partitions of `n`, as an *fmpz*.