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  "assumptions": [
    "Real principal root only. This engine does not return complex values.",
    "Index n is a positive safe integer (1st, square, cube, 4th, …, nth root). Generalized powers a^(1/n) with non-integer, negative, or non-safe-integer n belong on the Exponent calculator.",
    "Even n requires a ≥ 0 and returns b ≥ 0. Odd n allows a < 0 (for example ∛(−8) = −2).",
    "n = 2 uses Math.sqrt. n = 3 uses Math.cbrt, returning an implementation-approximated binary64 result (including negatives). Other n use a^(1/n) for a ≥ 0, or −(|a|)^(1/n) for odd n and a < 0.",
    "The Square Root calculator is a different contract: √(x<0) returns the principal imaginary. This page rejects that case as NOT_REAL."
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  "limitations": [
    "n must be a positive safe integer → INVALID_INDEX",
    "Even roots of a < 0 → NOT_REAL (unlike square-root imaginary)",
    "Missing a → MISSING_REQUIRED_INPUT"
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    "Non-numeric, object, array, boolean, NaN, or Infinity inputs return INVALID_NUMBER.",
    "n that is not a positive safe integer (including n = 0, n < 0, non-integers such as 2.5, and n outside JavaScript's safe-integer range) returns INVALID_INDEX.",
    "a < 0 with even n returns NOT_REAL.",
    "a = 0 returns 0.",
    "Defensive guards exist for unexpected non-finite numerical outcomes (RESULT_OVERFLOW / RESULT_UNDERFLOW). Overflow or underflow is not expected for valid finite nth-root inputs."
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      "title": "NIST Digital Library of Mathematical Functions, Chapter 4",
      "section": "Logarithm, Exponential, Powers",
      "url": "https://dlmf.nist.gov/4",
      "supports": "nth root as the principal real value of a^(1/n) when it exists",
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      "section": "Powers: principal value z^a = exp(a ln z)",
      "url": "https://dlmf.nist.gov/4.2",
      "supports": "Principal a^(1/n) for a > 0. Negative a is restricted here to odd integer n so the result stays the real odd root, not the complex principal power.",
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      "publisher": "National Institute of Standards and Technology"
    },
    {
      "title": "CalculatorX mathematical conventions",
      "section": "Real nth root; even roots of negatives are NOT_REAL; n is a positive safe integer",
      "supports": "Distinct from the Square Root calculator’s principal-imaginary contract for x < 0. Polynomial roots belong on Quadratic. Non-integer or non-safe-integer n is a generalized power (Exponent), not this nth-root contract. Negative odd roots use −(−a)^(1/n).",
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