Find a square root, cube root or root of any positive integer index. Enter the radicand a and index n; the default index is 2.
Nth Root Calculator
ⁿ√a
Use n = 2 for a square root, n = 3 for a cube root, or any positive integer.
How to use the calculator
- Enter the number whose root you want in the Radicand field.
- Enter 2 for a square root, 3 for a cube root, or another positive integer as the Index.
- Select Calculate root to see the result.
- Select Clear to start again.
What is an nth root?
The nth root of a number a is the value x such that xⁿ = a. It can also be written as ⁿ√a = a^(1/n).
xⁿ = a · x = ⁿ√a = a1/n
- n = 2: Square root
- n = 3: Cube root
- n = 4: Fourth root
Examples
| Radicand (a) | Index (n) | Result | Check |
|---|---|---|---|
| 16 | 2 | 4 | 4² = 16 |
| 27 | 3 | 3 | 3³ = 27 |
| 81 | 4 | 3 | 3⁴ = 81 |
| 2 | 2 | ≈ 1.4142 | 1.4142² ≈ 2 |
| −8 | 3 | −2 | (−2)³ = −8 |
Frequently asked questions about roots
What is the nth root of a number?
It is the number x that gives a when raised to the power n. For example, the fourth root of 16 is 2 because 2⁴ = 16.
How do I calculate a square root?
Use index 2. The square root of 16 is 4 because 4² = 16.
How do I calculate a cube root?
Use index 3. The cube root of 27 is 3 because 3³ = 27.
Can a negative number have a real root?
Yes when the index is odd, such as ∛−8 = −2. With an even index, a negative radicand has no real root.
What does ⁿ√a mean?
The symbol denotes the nth root of a. n is the index and a is the radicand.
See also…
