Root Calculator
Square roots, cube roots, and any nth root of a value, computed together so you can compare them at a glance — for whenever you need more than the square-root button on a basic calculator.
Inputs
Result
4
√ = 16 · ∛ = 6.349604
How the root calculator works
The nth root of a value equals value^(1/n) — root-taking and fractional exponentiation are the same operation.
Square root (n=2) and cube root (n=3) are shown by default alongside whatever custom root n you enter.
Worked example: 4th root of 256
- 256^(1/4) = 4, since 4⁴ = 4×4×4×4 = 256.
- For comparison, √256 = 16 and ∛256 ≈ 6.3496 — each higher root pulls the result down toward 1 as n grows.
Common mistakes to avoid
Taking an even root of a negative number
The square root, 4th root, or any even root of a negative number has no real result — only odd roots (cube root, 5th root, etc.) are defined for negative inputs in the real numbers.
Confusing 'root' with 'divide by n'
The nth root of a value is not the same as dividing it by n — 256 ÷ 4 is 64, while the 4th root of 256 is 4. These are entirely different operations.
Frequently asked questions
Why does a negative number under an even root show no result?
No real number multiplied by itself an even number of times can produce a negative result, so even roots of negatives are undefined in the real number system.
Can I take a root of a fraction or decimal?
Yes — root-taking works the same way for any positive real number, whole or fractional.
How does this relate to the Exponent Calculator?
They're mathematical inverses: this tool finds the base given a result and a root, while the Exponent Calculator finds the result given a base and a power.
What's the largest root this can meaningfully compute?
Any positive integer root works; as n grows very large, the result approaches 1 for any value greater than 1, since higher and higher roots flatten toward that limit.
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