GEOMEAN(1,2) and SQRT(2) return adjacent values in retained build 20430 controls

FN-GEOMEAN-001: GEOMEAN(1,2) and SQRT(2) return adjacent values in retained build 20430 controls

Excel differs from the mathematical answer · measured · recorded 2026-11-06

In two retained build 20430 controls, GEOMEAN(1,2) returned 1.414213562373095 (0x3ff6a09e667f3bcc), while SQRT(2) returned 1.4142135623730951 (0x3ff6a09e667f3bcd). Both functions mathematically return the positive square root of two; the SQRT result is the nearest binary64 value. A fifteen-significant-digit display hides the difference.

Correct value: Exact rational comparison: 2 lies strictly between the squares of the lower and upper binary64 midpoints around 0x3ff6a09e667f3bcd. Therefore that value is the nearest binary64 square root of 2.

Basis: Two rows read directly from the landed regenerated W111 capture files. Both record Excel build 20430, Windows 64-bit, Compatibility Version 2 and exact-double bulk Value2 inputs, on 29 September 2026. The calls are to different functions in the same recorded environment class; this is not a comparison between builds and no fresh Excel calls were made.

Open: Whether other inputs or environments retain the same difference; the two rows do not certify whole-function agreement or identify private Excel code.