Math & Trig
Cube root and nth root formula: positive and negative numbers
Raise numbers to fractional exponent ^(1/n) for any root degree, and pair SIGN with ABS for negative odd roots.
Fractional exponents ^(1/3) and ^(1/n)
Because spreadsheets provide SQRT for square roots but no CUBEROOT function, compute any nth root by raising the number to the reciprocal exponent 1 / n—wrapping the exponent in parentheses: Value ^ (1 / RootDegree).
Fractional powers can leave small floating-point residuals. The examples round to six decimal places for readable checks; choose precision according to the application rather than assuming every result is exact.
| Value (A) | RootDegree (B) | Formula Pattern | Exact Root |
|---|---|---|---|
| 125 | 3 | ROUND(A2^(1/B2), 6) | 5 |
| 81 | 4 | ROUND(A3^(1/B3), 6) | 3 |
| -27 | 3 | SIGN(A4)*ROUND(ABS(A4)^(1/B4), 6) | -3 |
Safe negative odd roots and even-root domain errors
Real cube roots of negative numbers exist (-3 * -3 * -3 = -27), whereas real square or fourth roots of negative numbers do not (#NUM!). Writing SIGN(x) * (ABS(x) ^ (1/3)) computes negative odd roots reliably across JavaScript and spreadsheet engines.
=ROUND(A2 ^ (1 / B2), 6)Negative cube root and negative square root (#NUM!)
SIGN(-27) * ROUND(ABS(-27) ^ (1 / 3), 6) returns -3, while SQRT(-16) returns #NUM! because no real number squares to -16.
=SIGN(A4) * ROUND(ABS(A4) ^ (1 / B4), 6)Try the example
Use the original values or change them to test your understanding.