Find the nth root of any number with domain validation for even roots of negative values and exact-result detection.
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Result
Square root of 9 (exact).
How it works
The nth root of a number x is the value r such that rn = x. Computed as x1/n.
Also in Functions
Algebra
The root calculator finds the nth root of any number. Enter a value and a root degree to get the result instantly, with detection of exact integer results and domain warnings for even roots of negative numbers.
The nth root of a number x is the value y such that y raised to the power n equals x. For example, the 4th root of 81 is 3 because 3^4 = 81. Square roots (n = 2) and cube roots (n = 3) are the most common cases.
Even roots of negative numbers have no real solution — the square root of -4, for instance, is not a real number. Odd roots of negative numbers are valid: the cube root of -8 is -2 because (-2)^3 = -8.
y = x^(1/n)
The nth root of x equals x raised to the power 1/n.
This calculator handles real-valued roots only. Complex roots of negative numbers under even degrees are flagged but not computed. For very large values, floating-point precision may affect the last digits.
Frequently asked questions
A root is the inverse of a power. If 2^3 = 8, then the cube root of 8 is 2. Taking the nth root is equivalent to raising to the power 1/n.
Not in real numbers. The square root of -1 is the imaginary unit i. This calculator works with real numbers only and will flag even roots of negatives as out of domain.
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