Nth Root Calculator
ⁿ√x = x^(1/n). Generalizes square and cube roots to any positive integer n.
Result
5√x
2.000000
5-th root of 32.
- x32
- n5
- 5√x2.0000000000
- Verification2.0000^5 = 32.0000
- Perfect?Yes
Step-by-step
- 5√x = x^(1/5).
- = 32^0.2000 = 2.00000000.
How to use this calculator
- Enter x.
- Enter root degree n.
- Read decimal value.
About this calculator
The n-th root of x is the value v where v^n = x. ⁵√32 = 2 (because 2⁵ = 32). For odd n, real n-th roots exist for negatives: ⁵√(−32) = −2. For even n, only non-negative inputs have real roots — ⁴√(−16) is imaginary. Compute via x^(1/n). Used in geometry (cube → ∛volume = side), finance (annualized return from a multi-period total), and decibel-related calculations.
Frequently asked
Squaring (or any even power) always gives a non-negative result, so reversing it from a negative is impossible in real numbers.
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