diff --git a/specs/phase0/beacon-chain.md b/specs/phase0/beacon-chain.md
index bdfb078380..536bba3364 100644
--- a/specs/phase0/beacon-chain.md
+++ b/specs/phase0/beacon-chain.md
@@ -178,6 +178,7 @@ The following values are (non-configurable) constants used throughout the specif
 
 | Name | Value |
 | - | - |
+| `MAX_UINT_64` | `uint64(2**64 - 1)` |
 | `GENESIS_SLOT` | `Slot(0)` |
 | `GENESIS_EPOCH` | `Epoch(0)` |
 | `FAR_FUTURE_EPOCH` | `Epoch(2**64 - 1)` |
@@ -599,6 +600,8 @@ def integer_squareroot(n: uint64) -> uint64:
     """
     Return the largest integer ``x`` such that ``x**2 <= n``.
     """
+    if n == MAX_UINT_64:
+        return uint64(4294967295)
     x = n
     y = (x + 1) // 2
     while y < x:
diff --git a/tests/core/pyspec/eth2spec/test/phase0/unittests/math/__init__.py b/tests/core/pyspec/eth2spec/test/phase0/unittests/math/__init__.py
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/tests/core/pyspec/eth2spec/test/phase0/unittests/math/test_integer_squareroot.py b/tests/core/pyspec/eth2spec/test/phase0/unittests/math/test_integer_squareroot.py
new file mode 100644
index 0000000000..988de1657c
--- /dev/null
+++ b/tests/core/pyspec/eth2spec/test/phase0/unittests/math/test_integer_squareroot.py
@@ -0,0 +1,23 @@
+import random
+from math import isqrt
+from eth2spec.test.context import (
+    spec_test,
+    single_phase,
+    with_all_phases,
+)
+
+
+@with_all_phases
+@spec_test
+@single_phase
+def test_integer_squareroot(spec):
+    values = [0, 100, 2**64 - 2, 2**64 - 1]
+    for n in values:
+        uint64_n = spec.uint64(n)
+        assert spec.integer_squareroot(uint64_n) == isqrt(n)
+
+    rng = random.Random(5566)
+    for _ in range(10):
+        n = rng.randint(0, 2**64 - 1)
+        uint64_n = spec.uint64(n)
+        assert spec.integer_squareroot(uint64_n) == isqrt(n)