{
  "category": "Math and trigonometry functions",
  "display_name": "SQRT",
  "entry_kind": "built_in_function",
  "eval_api": {
    "method": "POST",
    "url": "https://handbook.dnacalc.com/api/eval"
  },
  "function_id": "FUNC.SQRT",
  "implementation_state": {
    "answer_bank": {
      "excel_builds": [
        "20430"
      ],
      "larger_numeric": 0,
      "last_bit": 0,
      "matched": 42801,
      "other_mismatch": 0,
      "refused": 2,
      "rows": 42803,
      "unread": 0,
      "worst_ulp": 0
    },
    "detail": "Of 42,806 recorded answers (42,803 in the answer bank and 3 workbook cells), 2 do not match: 2 are refused.",
    "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87",
    "in_catalogue": true,
    "state": "differs",
    "state_label": "Known larger differences",
    "summary": "Refuses 2 of 42,806 recorded calls; the rest match",
    "workbook_corpus": {
      "cells": 3,
      "matched": 3
    }
  },
  "implementations": [
    {
      "commit": "9e1884369a678158dd82d3d74188daf986995e87",
      "flavour": "excel-compatibility-candidate",
      "language": "Rust",
      "name": "CalcFunc",
      "own_code": [
        "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/math.rs#L107-L107",
        "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/sqrt_fn.rs#L3-L8"
      ],
      "repository": "https://github.com/DnaCalc/DnaCalc",
      "shared_code": [
        "catalogue/math::unary",
        "ported/excel_numeric::excel_sqrt_staged"
      ],
      "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/math.rs#L107-L107",
      "state": "differs",
      "suite": null,
      "summary": "Refuses 2 of 42,806 recorded calls; the rest match"
    }
  ],
  "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.SQRT.json",
  "name": "SQRT",
  "notes": [
    {
      "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.",
      "documentation": null,
      "evidence": [
        {
          "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2",
          "locator": "w111broad-20260929-GEOMEAN-00003",
          "note": "Recorded GEOMEAN(1,2) answer and capture provenance.",
          "path": "cache/w111-broad-regenerated-20260929/answers-geomean.json.gz",
          "repository": "CalcFunc-Evidence"
        },
        {
          "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2",
          "locator": "w111broad-20260929-SQRT-00014",
          "note": "Recorded SQRT(2) answer and capture provenance.",
          "path": "cache/w111-broad-regenerated-20260929/answers-sqrt.json.gz",
          "repository": "CalcFunc-Evidence"
        },
        {
          "commit": "da3ecc4fb19a3a5529708c311d0e8f05688ac165",
          "locator": "excel_root_x87",
          "note": "Current normalized LN, reciprocal and EXP root reconstruction.",
          "path": "crates/calc-func/src/ported/excel_numeric/x87_chains.rs",
          "repository": "DnaCalc"
        }
      ],
      "functions": [
        "FUNC.GEOMEAN",
        "FUNC.SQRT"
      ],
      "inferred": null,
      "kind": "excel-differs-from-math",
      "note_id": "FN-GEOMEAN-001",
      "open": [
        "Whether other inputs or environments retain the same difference; the two rows do not certify whole-function agreement or identify private Excel code."
      ],
      "recorded_on": "2026-11-06",
      "repros": [
        {
          "call": "GEOMEAN(1,2)",
          "correct": {
            "bits": "0x3ff6a09e667f3bcd",
            "display": "1.4142135623730951",
            "how": "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.",
            "kind": "number"
          },
          "excel": {
            "bits": "0x3ff6a09e667f3bcc",
            "display": "1.414213562373095",
            "kind": "number"
          },
          "input_route": "cell-value2",
          "inputs": [
            {
              "name": "number1",
              "value": {
                "bits": "0x3ff0000000000000",
                "display": "1",
                "kind": "number"
              }
            },
            {
              "name": "number2",
              "value": {
                "bits": "0x4000000000000000",
                "display": "2",
                "kind": "number"
              }
            }
          ],
          "recorded_in": "Excel 16.0 build 20430, Windows 64-bit (NT 10.00), Workbook Compatibility Version 2; CPU not recorded. Captured 29 September 2026.",
          "source": {
            "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2",
            "locator": "w111broad-20260929-GEOMEAN-00003",
            "note": "Capture provenance records exact-double bulk Value2 cell input.",
            "path": "cache/w111-broad-regenerated-20260929/answers-geomean.json.gz",
            "repository": "CalcFunc-Evidence"
          }
        },
        {
          "call": "SQRT(2)",
          "correct": null,
          "excel": {
            "bits": "0x3ff6a09e667f3bcd",
            "display": "1.4142135623730951",
            "kind": "number"
          },
          "input_route": "cell-value2",
          "inputs": [
            {
              "name": "number",
              "value": {
                "bits": "0x4000000000000000",
                "display": "2",
                "kind": "number"
              }
            }
          ],
          "recorded_in": "Excel 16.0 build 20430, Windows 64-bit (NT 10.00), Workbook Compatibility Version 2; CPU not recorded. Captured 29 September 2026.",
          "source": {
            "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2",
            "locator": "w111broad-20260929-SQRT-00014",
            "note": "Capture provenance records exact-double bulk Value2 cell input.",
            "path": "cache/w111-broad-regenerated-20260929/answers-sqrt.json.gz",
            "repository": "CalcFunc-Evidence"
          }
        }
      ],
      "schema": "efh.function-note/v1",
      "statement": "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.",
      "status": "measured",
      "title": "GEOMEAN(1,2) and SQRT(2) return adjacent values in retained build 20430 controls"
    },
    {
      "basis": "41,897 of 41,897 distinct normal positive recorded rows match. On the 164 rows where double and correct rounding differ, Excel follows double rounding every time. The subnormal row is 1 row, and no read-back of its input is recorded.",
      "documentation": null,
      "evidence": [
        {
          "commit": "b5ce0759bce6a30fff848a3d82035cadcad1aa49",
          "locator": "excel_sqrt_staged",
          "note": "the kernel in the product",
          "path": "crates/calc-func/src/ported/sqrt_fn.rs",
          "repository": "DnaCalc"
        }
      ],
      "functions": [
        "FUNC.SQRT"
      ],
      "inferred": null,
      "kind": "excel-differs-from-math",
      "note_id": "FN-SQRT-001",
      "open": [],
      "recorded_on": "2026-11-04",
      "repros": [
        {
          "call": "SQRT(0.9999999999999999)",
          "correct": {
            "bits": "0x3fefffffffffffff",
            "display": "0.9999999999999999",
            "how": "Exact square root at 800 bits, correctly rounded.",
            "kind": "number"
          },
          "excel": {
            "bits": "0x3ff0000000000000",
            "display": "1",
            "kind": "number"
          },
          "input_route": "cell-value2",
          "inputs": [
            {
              "name": "number",
              "value": {
                "bits": "0x3fefffffffffffff",
                "display": "0.9999999999999999",
                "kind": "number"
              }
            }
          ],
          "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture",
          "source": {
            "commit": "4d5320dfdc385354469b4d506153357bb932ab08",
            "locator": "w111broad-20260929-SQRT-00016",
            "note": null,
            "path": "runs/w111-broad-20260929/answers/answers-sqrt.json.gz",
            "repository": "CalcFunc-Evidence"
          }
        },
        {
          "call": "SQRT(1.7976931348623157e+308)",
          "correct": {
            "bits": "0x5fefffffffffffff",
            "display": "1.3407807929942596e+154",
            "how": "Exact square root at 800 bits, correctly rounded.",
            "kind": "number"
          },
          "excel": {
            "bits": "0x5ff0000000000000",
            "display": "1.3407807929942597e+154",
            "kind": "number"
          },
          "input_route": "cell-value2",
          "inputs": [
            {
              "name": "number",
              "value": {
                "bits": "0x7fefffffffffffff",
                "display": "1.7976931348623157e+308",
                "kind": "number"
              }
            }
          ],
          "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture",
          "source": {
            "commit": "4d5320dfdc385354469b4d506153357bb932ab08",
            "locator": "w111broad-20260929-SQRT-00025",
            "note": null,
            "path": "runs/w111-broad-20260929/answers/answers-sqrt.json.gz",
            "repository": "CalcFunc-Evidence"
          }
        },
        {
          "call": "SQRT(5e-324)",
          "correct": null,
          "excel": {
            "bits": "0x0000000000000000",
            "display": "0",
            "kind": "number"
          },
          "input_route": "cell-value2",
          "inputs": [
            {
              "name": "number",
              "value": {
                "bits": "0x0000000000000001",
                "display": "5e-324",
                "kind": "number"
              }
            }
          ],
          "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture",
          "source": {
            "commit": "4d5320dfdc385354469b4d506153357bb932ab08",
            "locator": "w111broad-20260929-SQRT-00002",
            "note": null,
            "path": "runs/w111-broad-20260929/answers/answers-sqrt.json.gz",
            "repository": "CalcFunc-Evidence"
          }
        }
      ],
      "schema": "efh.function-note/v1",
      "statement": "The worksheet SQRT is RN53(RN64(sqrt(x))): the root is rounded to the x87 unit's 64-bit significand and then stored to binary64. On inputs where that double rounding lands differently from a single rounding, Excel takes the double-rounded value: SQRT(0.9999999999999999) is 1. A subnormal written to a cell reads back as 0, so the 0 for the smallest subnormal below may record that and not SQRT.",
      "status": "measured",
      "title": "SQRT is rounded twice, once to 64 bits and once to 53"
    },
    {
      "basis": "66 recorded VALUE readings (all ten digits of each of the five scripts, then composed forms), 10 SQRT and 4 DATEVALUE readings.",
      "documentation": null,
      "evidence": [
        {
          "commit": "55697ab4f74bab852fef7bc76b08588c3a5f408e",
          "locator": "delivered_fn4_digit_scripts_and_numeric_date_widths",
          "note": "recorded answers pinned",
          "path": "apps/dna-onecalc/tests/acceptance.rs",
          "repository": "DnaCalc"
        },
        {
          "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
          "locator": "sheets qt031 to qt096",
          "note": "66 recorded readings",
          "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json",
          "repository": "DnaCalc"
        },
        {
          "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
          "locator": null,
          "note": "10 recorded readings",
          "path": "crates/calc-func/tests/captures/fn4_questions/SQRT.reading.json",
          "repository": "DnaCalc"
        },
        {
          "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
          "locator": null,
          "note": "6 recorded readings",
          "path": "crates/calc-func/tests/captures/fn4_questions/DATEVALUE.reading.json",
          "repository": "DnaCalc"
        }
      ],
      "functions": [
        "FUNC.DATEVALUE",
        "FUNC.SQRT",
        "FUNC.VALUE"
      ],
      "inferred": "That other text-to-number routes, such as arithmetic operators, treat digits the same way is inferred from VALUE and SQRT agreeing.",
      "kind": "quirk",
      "note_id": "FN-VALUE-001",
      "open": [
        "Other digit blocks (Bengali, Tibetan, Khmer and so on) have not been read.",
        "Whether the set depends on the Windows or workbook locale has not been read."
      ],
      "recorded_on": "2026-11-04",
      "repros": [
        {
          "call": "=VALUE(\"١\")",
          "correct": null,
          "excel": {
            "bits": "0x3ff0000000000000",
            "display": "1",
            "kind": "number"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA",
          "source": {
            "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
            "locator": "sheet qt042, row 20, column 10",
            "note": null,
            "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json",
            "repository": "DnaCalc"
          }
        },
        {
          "call": "=VALUE(\"١٢٣\")",
          "correct": null,
          "excel": {
            "bits": "0x405ec00000000000",
            "display": "123",
            "kind": "number"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA",
          "source": {
            "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
            "locator": "sheet qt081, row 20, column 10",
            "note": null,
            "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json",
            "repository": "DnaCalc"
          }
        },
        {
          "call": "=VALUE(\"1٢3\")",
          "correct": null,
          "excel": {
            "bits": "0x405ec00000000000",
            "display": "123",
            "kind": "number"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA",
          "source": {
            "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
            "locator": "sheet qt084, row 20, column 10",
            "note": null,
            "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json",
            "repository": "DnaCalc"
          }
        },
        {
          "call": "=VALUE(\"١e2\")",
          "correct": null,
          "excel": {
            "bits": "0x4059000000000000",
            "display": "100",
            "kind": "number"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA",
          "source": {
            "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
            "locator": "sheet qt088, row 20, column 10",
            "note": null,
            "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json",
            "repository": "DnaCalc"
          }
        },
        {
          "call": "=VALUE(\"१\")",
          "correct": null,
          "excel": {
            "bits": "0x3ff0000000000000",
            "display": "1",
            "kind": "number"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA",
          "source": {
            "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
            "locator": "sheet qt062, row 20, column 10",
            "note": null,
            "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json",
            "repository": "DnaCalc"
          }
        },
        {
          "call": "=VALUE(\"๑\")",
          "correct": null,
          "excel": {
            "bits": "0x3ff0000000000000",
            "display": "1",
            "kind": "number"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA",
          "source": {
            "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
            "locator": "sheet qt072, row 20, column 10",
            "note": null,
            "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json",
            "repository": "DnaCalc"
          }
        },
        {
          "call": "=VALUE(\"１\")",
          "correct": null,
          "excel": {
            "bits": null,
            "display": "#VALUE!",
            "kind": "error"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA",
          "source": {
            "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
            "locator": "sheet qt032, row 20, column 10",
            "note": null,
            "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json",
            "repository": "DnaCalc"
          }
        },
        {
          "call": "=VALUE(\"1２3\")",
          "correct": null,
          "excel": {
            "bits": null,
            "display": "#VALUE!",
            "kind": "error"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA",
          "source": {
            "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
            "locator": "sheet qt093, row 20, column 10",
            "note": null,
            "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json",
            "repository": "DnaCalc"
          }
        },
        {
          "call": "=SQRT(\"۱٢३๔\")",
          "correct": null,
          "excel": {
            "bits": "0x4041906d51932c26",
            "display": "35.12833614050059",
            "kind": "number"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088, Windows, bitness and CPU not recorded in this reading file",
          "source": {
            "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
            "locator": "fn7-SQRT-digits-6",
            "note": null,
            "path": "crates/calc-func/tests/captures/fn4_questions/SQRT.reading.json",
            "repository": "DnaCalc"
          }
        },
        {
          "call": "=DATEVALUE(\"٢٠٢٤-٠١-٠٢\")",
          "correct": null,
          "excel": {
            "bits": "0x40e61da000000000",
            "display": "45293",
            "kind": "number"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088, Windows, bitness and CPU not recorded in this reading file",
          "source": {
            "commit": "2d0eddcac86413014643af81d646581d54ba57bc",
            "locator": "fn7-DATEVALUE-digits-1",
            "note": null,
            "path": "crates/calc-func/tests/captures/fn4_questions/DATEVALUE.reading.json",
            "repository": "DnaCalc"
          }
        }
      ],
      "schema": "efh.function-note/v1",
      "statement": "In the recorded en-ZA settings, converting text to a number accepts Arabic-Indic (U+0660 to U+0669), extended Arabic-Indic (U+06F0 to U+06F9), Devanagari (U+0966 to U+096F) and Thai (U+0E50 to U+0E59) digits. They work alone, in runs, with a decimal point, in the exponent, with a sign or percent, and mixed with ASCII digits or with each other: VALUE(\"1٢3\") is 123, and SQRT of a four-digit string using four scripts is the root of 1234. Fullwidth digits (U+FF10 to U+FF19) give #VALUE! alone or mixed. DATEVALUE reads the four accepted scripts in a date written year-month-day.",
      "status": "measured",
      "title": "Text to number reads Arabic, Persian, Devanagari and Thai digits, but not fullwidth digits"
    }
  ],
  "schema": "efh.function-reference/v1",
  "section_order": [
    "what-it-does",
    "try-it",
    "quirks",
    "how-to-implement",
    "version-differences",
    "alternatives"
  ],
  "sections": {
    "alternatives": "\n[IMSQRT](FUNC.IMSQRT.md) accepts complex inputs. [SQRTPI](FUNC.SQRTPI.md) includes a multiplication by pi, and [IMABS](FUNC.IMABS.md) uses a hypotenuse route for complex magnitude. [POWER](FUNC.POWER.md) accepts other exponents but must retain its own numerical graph.\n\n\n\n\n",
    "how-to-implement": "\nFor the finite nonnegative scalar route, reject negative inputs before the root and return zero for zero. For positive x:\n\n1. Find the exponent of the root by halving `floor(log2(x))`, rounding downward. Obtain the input exponent from its bits or exact comparisons.\n2. Round the exact square root to a 64-bit significand, ties-to-even. The [portable staged-root recipe](../model/09-staged-arithmetic.md#square-root-without-an-extended-host-type) finds this with an integer square root and an exact comparison against a squared midpoint. It needs no host extended floating-point type.\n3. Store that rounded root to binary64, again choosing nearest/even. Keep this second step; directly calling a binary64 sqrt removes the recorded first rounding.\n\nWorked boundary: `x=1-2^-53`. The midpoint between its two possible binary64 root results is `m=1-2^-54`. Since `m*m=x+2^-108`, the true root is slightly below m. Rounding it first to 64 significant bits gives m; the binary64 midpoint tie then selects one, whose low significand bit is even. A direct binary64 root instead selects `1-2^-53`.\n\nFN-SQRT-001 reports 41,897 matching distinct normal-positive recorded inputs, including all 164 controls where the staged and single-rounding roots differ. Its reproductions name Excel build 20430 on Windows 64-bit. These results support the stated staged route on that evidence, with no published Handbook suite or whole-domain equality claim. The input route and worksheet publication remain separate from the root primitive.\n\n\n",
    "quirks": "\nRecorded worksheet SQRT uses a root rounded to a 64-bit significand followed by a binary64 store. That can differ by a final bit from one correctly rounded binary64 square root. In the exact-cell control `0x3fefffffffffffff` (`0.9999999999999999`), Excel returns one; a single-rounding mathematical reference returns the preceding binary64 value.\n\nThe smallest-subnormal reproduction returned zero, but its cell input was not read back. That observation does not establish a square-root underflow rule: input transfer may already have changed it to zero. A positive finite root itself fits the binary64 normal range even for the smallest positive binary64 input.\n\nCompositions need their own operation order. Squaring two large components before SQRT can overflow when a scaled hypotenuse would be finite. A general POWER route or a logarithm/exponential composition also has different intermediate rounding.\n\n\n",
    "sources": "\n- [Microsoft: SQRT function](https://support.microsoft.com/en-us/excel/functions/sqrt-function), opened 6 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/excel_numeric/mod.rs); implementation steps and the limits identified in the text.\n- [FN-SQRT-001](../notes/FN-SQRT-001.json): exact inputs, recorded results and the subnormal transfer limit.\n- [Software extended root and binary64 store](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/excel_numeric/soft87.rs).\n- [FN-GEOMEAN-001](../notes/FN-GEOMEAN-001.json): two retained build 20430 controls, with a rational check of the nearest square root.\n\n",
    "try-it": "\n`=SQRT(81)` returns `9`; `=SQRT(2)` is about `1.414213562373095`. Squaring the returned binary64 value need not recover the input exactly.\n\n`=SQRT(-9)` gives `#NUM!`. `=SQRT(ABS(-9))` returns three because it changes the input to positive nine. Use IMSQRT when a complex root of the original negative value is intended.\n\nThe retained build 20430 controls give `GEOMEAN(1,2)=1.414213562373095` and `SQRT(2)=1.4142135623730951`, adjacent binary64 values. [FN-GEOMEAN-001](../notes/FN-GEOMEAN-001.json) retains the exact cell inputs and both answers. Their mathematical values agree, but the recorded calculation routes do not publish the same bits.\n\n\n",
    "version-differences": "The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.\n\n| Excel 16.0 build | Platform and CPU | Captured inputs |\n|---|---|---:|\n| 19929 | Windows, bitness not recorded, CPU not recorded | 42 |\n| 20430 | Windows, 64-bit, CPU not recorded | 42,803 |\n\n- XC-SQRT-001: build 19929 versus build 20430; 2 same-input pairs, 0 differing answers. Compared axes: excel-build. Numeric answers were compared by their recorded binary64 bits; other answers by typed value.\n\nAgreement on these compared inputs does not establish agreement on unmeasured inputs.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.SQRT.json).\n\nRetained controls from the indexed captures:\n\n| Build and recorded CPU | Captured call or arguments | Excel result |\n|---|---|---|\n| 19929, CPU not recorded | [`=SQRT(0)`](https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/runs/broad-scalar-cycle-011-cellref/comparisons/excel_sample_comparisons.jsonl.gz) | `0.0` (`0x0000000000000000`) |\n| 20430, CPU not recorded | [`SQRT(2)`](https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/cache/w111-broad-regenerated-20260929/answers-sqrt.json.gz) | `1.4142135623730951` (`0x3ff6a09e667f3bcd`) |\n\nThese are earlier recorded answers, not new Excel runs or an additional cross-build comparison. The function JSON retains each source locator, exact argument bits where available, and input-route status. Call notation does not imply that captured binary64 values were entered as decimal formula literals.",
    "what-it-does": "\n`SQRT(number)` returns the nonnegative real square root. A positive input has two mathematical real roots; this function chooses the positive one. Zero returns zero. Microsoft documents `#NUM!` for a negative input.\n\n\n"
  },
  "signature": {
    "display": "SQRT(number)",
    "parameters": [
      {
        "description": null,
        "name": "number",
        "optional": false,
        "repeats": false
      }
    ],
    "trailing_repeats": false
  },
  "sources": {
    "metadata": {
      "admission": {
        "label": "implemented",
        "reason": null
      },
      "arity": {
        "max": 1,
        "min": 1
      },
      "category": "Math and trigonometry functions",
      "classification": {
        "arg_preparation_profile": "ValuesOnlyPreAdapter",
        "coercion_lift_profile": "UnaryNumericScalarOrArrayElementwise",
        "determinism_class": "Deterministic",
        "error_collapse_profile": "None",
        "fec_dependency_profile": "None",
        "host_interaction_class": "None",
        "kernel_signature_class": "Custom",
        "rich_value_usage": "RichBlind",
        "surface_fec_dependency_profile": "RefOnly",
        "thread_safety_class": "SafePure",
        "volatility_class": "NonVolatile"
      },
      "descriptions": {
        "long": null,
        "short": "Square root of a number that is zero or more",
        "short_source": "dna-calc-own"
      },
      "docs": {
        "english_description": "Returns a positive square root",
        "microsoft_url": "https://support.microsoft.com/en-us/office/sqrt-function-654975c2-05c4-4831-9a24-2c65e4040fdf"
      },
      "entry_kind": "built_in_function",
      "localized_family_names": null,
      "localized_names": [
        {
          "locale": "ar-SA",
          "name": "SQRT"
        },
        {
          "locale": "bg-BG",
          "name": "SQRT"
        },
        {
          "locale": "cs-CZ",
          "name": "SQRT"
        },
        {
          "locale": "da-DK",
          "name": "KVROD"
        },
        {
          "locale": "de-DE",
          "name": "WURZEL"
        },
        {
          "locale": "el-GR",
          "name": "SQRT"
        },
        {
          "locale": "en-AU",
          "name": "SQRT"
        },
        {
          "locale": "en-GB",
          "name": "SQRT"
        },
        {
          "locale": "en-US",
          "name": "SQRT"
        },
        {
          "locale": "es-ES",
          "name": "RAIZ"
        },
        {
          "locale": "et-EE",
          "name": "SQRT"
        },
        {
          "locale": "fi-FI",
          "name": "NELIÖJUURI"
        },
        {
          "locale": "fr-FR",
          "name": "RACINE"
        },
        {
          "locale": "he-IL",
          "name": "SQRT"
        },
        {
          "locale": "hr-HR",
          "name": "SQRT"
        },
        {
          "locale": "hu-HU",
          "name": "GYÖK"
        },
        {
          "locale": "id-ID",
          "name": "SQRT"
        },
        {
          "locale": "it-IT",
          "name": "RADQ"
        },
        {
          "locale": "ja-JP",
          "name": "SQRT"
        },
        {
          "locale": "ko-KR",
          "name": "SQRT"
        },
        {
          "locale": "lt-LT",
          "name": "SQRT"
        },
        {
          "locale": "lv-LV",
          "name": "SQRT"
        },
        {
          "locale": "nb-NO",
          "name": "ROT"
        },
        {
          "locale": "nl-NL",
          "name": "WORTEL"
        },
        {
          "locale": "pl-PL",
          "name": "SQRT"
        },
        {
          "locale": "pt-BR",
          "name": "RAIZ"
        },
        {
          "locale": "pt-PT",
          "name": "RAIZQ"
        },
        {
          "locale": "ro-RO",
          "name": "SQRT"
        },
        {
          "locale": "ru-RU",
          "name": "КОРЕНЬ"
        },
        {
          "locale": "sk-SK",
          "name": "SQRT"
        },
        {
          "locale": "sl-SI",
          "name": "SQRT"
        },
        {
          "locale": "sr-Latn-RS",
          "name": "SQRT"
        },
        {
          "locale": "sv-SE",
          "name": "ROT"
        },
        {
          "locale": "th-TH",
          "name": "SQRT"
        },
        {
          "locale": "tr-TR",
          "name": "KAREKÖK"
        },
        {
          "locale": "uk-UA",
          "name": "SQRT"
        },
        {
          "locale": "vi-VN",
          "name": "SQRT"
        },
        {
          "locale": "zh-CN",
          "name": "SQRT"
        },
        {
          "locale": "zh-HK",
          "name": "SQRT"
        },
        {
          "locale": "zh-TW",
          "name": "SQRT"
        }
      ],
      "signature": {
        "display": "SQRT(number)",
        "parameters": [
          {
            "description": null,
            "name": "number",
            "optional": false,
            "repeats": false
          }
        ],
        "trailing_repeats": false
      },
      "surface_name": "SQRT",
      "version_marker": null,
      "xlcall": {
        "code": "20",
        "symbol": "xlfSqrt"
      }
    },
    "microsoft": "https://support.microsoft.com/en-us/office/sqrt-function-654975c2-05c4-4831-9a24-2c65e4040fdf"
  },
  "try_it": {
    "formula": "=SQRT(81)"
  },
  "url": "https://handbook.dnacalc.com/functions/SQRT.html",
  "variants": [],
  "versions": [
    {
      "behaviour": "SQRT(0.9999999999999999) returned 1 (0x3ff0000000000000). SQRT(1.7976931348623157e+308) returned 1.3407807929942597e+154 (0x5ff0000000000000). 1 further recorded control is attached. Inputs were supplied through cells using Value2. These are controls from this environment, not a same-input comparison with another build.",
      "excel_build": "16.0 build 20430",
      "observations": [
        {
          "call": "SQRT(0.9999999999999999)",
          "excel": {
            "bits": "0x3ff0000000000000",
            "display": "1",
            "kind": "number"
          },
          "input_route": "cell-value2",
          "inputs": [
            {
              "name": "number",
              "value": {
                "bits": "0x3fefffffffffffff",
                "display": "0.9999999999999999",
                "kind": "number"
              }
            }
          ],
          "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture"
        },
        {
          "call": "SQRT(1.7976931348623157e+308)",
          "excel": {
            "bits": "0x5ff0000000000000",
            "display": "1.3407807929942597e+154",
            "kind": "number"
          },
          "input_route": "cell-value2",
          "inputs": [
            {
              "name": "number",
              "value": {
                "bits": "0x7fefffffffffffff",
                "display": "1.7976931348623157e+308",
                "kind": "number"
              }
            }
          ],
          "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture"
        },
        {
          "call": "SQRT(5e-324)",
          "excel": {
            "bits": "0x0000000000000000",
            "display": "0",
            "kind": "number"
          },
          "input_route": "cell-value2",
          "inputs": [
            {
              "name": "number",
              "value": {
                "bits": "0x0000000000000001",
                "display": "5e-324",
                "kind": "number"
              }
            }
          ],
          "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture"
        }
      ],
      "platform": "Windows 64-bit, CPU not recorded in this capture",
      "sources": [
        "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/3345a87/content/notes/FN-SQRT-001.json"
      ]
    },
    {
      "behaviour": "=SQRT(\"۱٢३๔\") returned 35.12833614050059 (0x4041906d51932c26). Inputs were supplied through formula literals. These are controls from this environment, not a same-input comparison with another build.",
      "excel_build": "16.0.20527.20088",
      "observations": [
        {
          "call": "=SQRT(\"۱٢३๔\")",
          "excel": {
            "bits": "0x4041906d51932c26",
            "display": "35.12833614050059",
            "kind": "number"
          },
          "input_route": "formula-literal",
          "inputs": [],
          "recorded_in": "Excel 16.0.20527.20088, Windows, bitness and CPU not recorded in this reading file"
        }
      ],
      "platform": "Windows, bitness and CPU not recorded in this reading file",
      "sources": [
        "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/3345a87/content/notes/FN-VALUE-001.json"
      ]
    },
    {
      "behaviour": "42 captured inputs are indexed for this environment. Capture dates are not recorded. This is a reading count, not a comparison with another build. Retained control =SQRT(0) returned 0.0 (0x0000000000000000). The selected archive row does not record its input plumbing; no input route is inferred.",
      "excel_build": "16.0 build 19929",
      "observations": [
        {
          "call": "=SQRT(0)",
          "excel": {
            "bits": "0x0000000000000000",
            "display": "0.0",
            "kind": "number"
          },
          "input_route": "not-recorded",
          "inputs": [],
          "recorded_in": "Excel 16.0 build 19929, Windows, bitness not recorded, CPU not recorded.",
          "source": {
            "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2",
            "locator": "BSE-000000622",
            "path": "runs/broad-scalar-cycle-011-cellref/comparisons/excel_sample_comparisons.jsonl.gz",
            "repository": "CalcFunc-Evidence"
          }
        }
      ],
      "platform": "Windows, bitness not recorded, CPU not recorded",
      "sources": [
        "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.SQRT.json",
        "https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/runs/broad-scalar-cycle-011-cellref/comparisons/excel_sample_comparisons.jsonl.gz"
      ]
    },
    {
      "behaviour": "42,803 captured inputs are indexed for this environment. Capture dates: 2026-09-29 to 2026-09-29. This is a reading count, not a comparison with another build. Retained control SQRT(2) returned 1.4142135623730951 (0x3ff6a09e667f3bcd). The capture specifies exact-double bulk Value2 cell input.",
      "excel_build": "16.0 build 20430",
      "observations": [
        {
          "call": "SQRT(2)",
          "excel": {
            "bits": "0x3ff6a09e667f3bcd",
            "display": "1.4142135623730951",
            "kind": "number"
          },
          "input_route": "cell-value2",
          "inputs": [
            {
              "name": "argument1",
              "value": {
                "bits": "0x4000000000000000",
                "display": "2",
                "kind": "number"
              }
            }
          ],
          "recorded_in": "Excel 16.0 build 20430, Windows, 64-bit, CPU not recorded.",
          "source": {
            "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2",
            "locator": "w111broad-20260929-SQRT-00014",
            "path": "cache/w111-broad-regenerated-20260929/answers-sqrt.json.gz",
            "repository": "CalcFunc-Evidence"
          }
        }
      ],
      "platform": "Windows, 64-bit, CPU not recorded",
      "sources": [
        "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.SQRT.json",
        "https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/cache/w111-broad-regenerated-20260929/answers-sqrt.json.gz"
      ]
    }
  ]
}