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Nth Root Calculator

Computes the principal n-th root of a number (value^(1/n)), returning the real negative root for odd n and the second, negative root for even n.

When to use

You need √x, ∛x or any integer-degree root, including odd roots of negative numbers.

Do not use when: You need a fractional power such as x^(2/3) (use exponent) or the solutions of a quadratic (use quadratic-equation).

root = |value|^(1/n) × sign(value); for even n and value > 0 the roots are ±root

Roots that are exact integers are snapped to the integer when |value|^(1/n) is within 10^-9 of it and the integer power reproduces value exactly.

Parameter	Type	Unit	Required	Description
`value`	number		yes	The number under the root sign. Negative values are allowed only for odd n. Range: ≥ -1e+300, ≤ 1e+300
`n`	integer		yes	2 for square root, 3 for cube root, etc. Range: ≥ 1, ≤ 1000

Output	Type	Description
`root`	number	The real n-th root with the same sign as value.
`negative_root`	number	−root: the second real root, present only for even n and positive value.
`verification`	number	The root raised back to the n-th power (should equal value).
`expression`	string	The root as text, e.g. '16^(1/4) = 2'.

Fourth root of 16: {"value":16,"n":4} → {"root":2,"negative_root":-2,"verification":16,"expression":"16^(1/4) = 2"}

Fifth root of −32: {"value":-32,"n":5} → {"root":-2,"verification":-32}

GET https://tttkmbb.com/api/v1/calculate/nth-root?value=16&n=4

API: GET https://tttkmbb.com/api/v1/calculate/nth-root (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/nth-root · Markdown: https://tttkmbb.com/math/nth-root.md · JSON definition: https://tttkmbb.com/math/nth-root.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="nth-root"
OpenAPI operationId: calculate_nth_root
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Even roots of negative numbers are imaginary (√−4 = 2i); only odd roots of negatives are real, e.g. ∛−27 = −3.

Both 2 and −2 satisfy x⁴ = 16. The principal root is the positive one; negative_root gives the other.