Radical Calculator — nth Root of Any Number
A radical (ⁿ√x) is the inverse of raising a number to the nth power. Enter the radicand (the number under the radical sign) and the root index n to get the exact result, plus the result squared and cubed for quick verification.
The nth root of the radicand
- 1
Reciprocal exponent (1 ÷ n)
1 ÷ 3 = 0.333333 - 2
Apply: ⁿ√x = x^(1/n)
64^(0.333333) = 4
How does this calculator work?
ⁿ√x = x^(1/n): enter the radicand (x) and root index (n) to compute any radical. Square root uses n = 2, cube root n = 3. Even roots of negative numbers have no real solution. The result r satisfies rⁿ = x and can be verified by powering it back up.
Formula
How this is calculated
The nth root of x is the number r such that rⁿ = x. It is computed as x^(1/n), i.e. raising x to the reciprocal of the index. The square root uses n = 2 and the cube root uses n = 3; any positive integer (or decimal) index is accepted.
For positive radicands the result is always positive. For negative radicands the root is real only when n is an odd integer — for example ³√(−8) = −2 because (−2)³ = −8. Even roots of negative numbers (such as √(−4)) are imaginary and are not computed here.
To verify: multiply the result by itself n times — it should equal the original radicand (modulo rounding). The calculator also shows result² and result³ for quick sanity-checking.
Frequently asked questions
A radical is the symbol √ (or ⁿ√ for higher roots) representing the nth root operation. The number inside is the radicand; the small number above-left is the index. Without an index, √ means the square root (index 2).
An even root of a negative number has no real solution because any real number raised to an even power is non-negative. For example, there is no real x with x² = −4. The answer exists in the complex number system as an imaginary number.
Factor out perfect squares: 72 = 36 × 2, so √72 = √36 × √2 = 6√2 ≈ 8.485. This calculator gives the decimal result; for symbolic simplification, look for the largest perfect-square factor of the radicand.
Also known as
TG we-Calculate Editorial Team. (2026). Radical Calculator — nth Root of Any Number [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/radical-calculator
TG we-Calculate Editorial Team. "Radical Calculator — nth Root of Any Number." TG we-Calculate. 2026. https://we-calculate.com/calculator/radical-calculator.
TG we-Calculate Editorial Team, "Radical Calculator — nth Root of Any Number," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/radical-calculator
@misc{wecalculate_radical_calculator, title = {Radical Calculator — nth Root of Any Number}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/radical-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?