How to Calculate Nth Root
What is Nth Root?
The nth root of a number x is the value r such that rⁿ = x. The square root is the 2nd root; cube root is the 3rd root. For even roots of negative numbers, no real solution exists (result is a complex number).
Formula
- x
- x^(1/3) — x^(1/3)
Step-by-Step Guide
- 1ⁿ√x = x^(1/n)
- 2Square root: ²√x = x^0.5
- 3Cube root: ³√x = x^(1/3)
- 4Nth root: use x^(1/n) on a calculator
- 5Negative numbers: odd roots are fine (³√−8 = −2); even roots are complex
Worked Examples
Frequently Asked Questions
What is Nth Root?
The nth root of a number x is the value r such that rⁿ = x. The square root is the 2nd root; cube root is the 3rd root
How accurate is the Nth Root calculator?
The calculator uses the standard published formula for nth root. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.
What units does the Nth Root calculator use?
This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.
What formula does the Nth Root calculator use?
The core formula is: ⁿ√x = x^(1/n). Each step in the calculation is shown so you can verify the result manually.