Calculate an nth root and simplify integer radicals, including real odd roots of negative numbers.
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1 – 100
2th root
8.48528137
Simplified radical6√(2)
How this was calculated
x = sign(a) × |a|^(1/n) = 8.48528137. Even roots use the nonnegative principal root.
Solving xⁿ = a is different: when n is even and a > 0, both +8.48528137 and −8.48528137 satisfy the equation.
Formula and method
The nth root of a satisfies xⁿ = a. The calculator returns the principal nonnegative root for an even index and the signed real root for an odd index. Factorization extracts groups of n equal prime factors from an integer radical.
Worked example
72 = 2³ × 3², so √72 = 6√2 ≈ 8.48528137. The cube root of −125 is −5.
Inputs and limitations
An even root of a negative number is not real. The index must be an integer from 1 to 100. Exact radical simplification is limited to integer radicands with magnitude at most 10¹²; larger or decimal values receive a numerical root.
Last updated . Results are estimates for informational purposes only.