Square root, cube root and nth root calculator
Enter the number and the index n of the root (2 for a square root, 3 for a cube root…). Choose real or complex mode.
Result
3Root
- Exact result: 3^3 = 27.
Inputs
- Number
- 27
- Root index n
- 3
- Mode
- Real
How it is calculated
The nth root of x is the number r with r^n = x, so r = x^(1/n).
Result
Root
How it is calculated
- The nth root of x is the number r with r^n = x, so r = x^(1/n).
- Odd index: a real root always exists, with the same sign as x.
- Even index and negative x: no real root. In complex mode: r = |x|^(1/n) × (cos(π/n) + i sin(π/n)).
Example
Cube root of 27: 3, because 3³ = 27.
Good to know
- In real mode, an even root of a negative number is refused.
- Results use decimal numbers: about 15 exact digits.
Frequently asked questions
What is this tool used for?
Enter the number and the index n of the root (2 for a square root, 3 for a cube root…). Choose real or complex mode.
How is the result calculated?
The nth root of x is the number r with r^n = x, so r = x^(1/n).
What should I check before using the result?
In real mode, an even root of a negative number is refused.