Root Calculator
Enter a number and a degree to find its nth root ⁿ√x — square root by default, with the working shown.
Reviewed by the OmniCalc teamMethod verified 2026-07-01
4
Root 4Show steps
- Rewrite the root as a power: ⁿ√x = x^(1/n).
- Substitute the number x = 16 and the degree n = 2: 16^(1/2).
- Evaluate: 16^(1/2) = 4.
How to use the root calculator
- 1Enter the number (x) — the value you want the root of.
- 2Enter the degree (n) — 2 for a square root, 3 for a cube root, and so on. It defaults to 2.
- 3Read the answer ⁿ√x, computed instantly.
- 4Open Show steps under the result to see the exact working.
Only odd degrees reach negative numbers
Every positive number has a root for any degree, but a negative number only does when the degree is an odd whole number: ∛−8 = −2, yet √−4 has no real answer. Even and fractional degrees of a negative show a dash, not a wrong number.
Frequently asked questions
What is the nth root of a number?
The nth root of a number x is the value that, raised to the power n, gives back x. It is the same as x^(1/n): a degree of 2 is the square root, a degree of 3 is the cube root, and so on.
Why does a negative number sometimes have no root?
A negative number has a real root only when the degree is an odd integer — the cube root of −8 is −2. With an even degree such as a square root, or a fractional degree, no real number works, so the calculator shows a dash instead of a wrong answer.
How is a root related to an exponent?
They are inverses: raising to the power n and taking the nth root undo each other, so (ⁿ√x)ⁿ = x. That is why the nth root is written as the fractional power x^(1/n) — a root is just a power with a reciprocal exponent.
How do I take a cube root or higher?
Set the degree to 3 for a cube root, 4 for a fourth root, and so on. Any degree works, including decimals and negative degrees, where a negative degree gives a reciprocal root such as 4^(1/−2) = 0.5.