Example 1
- x = 27
- n = 3
3
What is ³√27? 3. Three cubed is 27.
Nth root calculator
Type x and the degree n. 27 and 3 give 3, because 3³ = 27. 16 and 2 give 4. 81 and 4 give 3. When n = 0 the result is 0.
The calculator takes the nth root of x. When n = 0 the formula returns 0, not a blank and not Infinity. A negative x with a fractional 1/n often leaves a blank, because power returns a blank value.
Results
Enter data and click Calculate.
How it works
The nth root looks for a y such that yⁿ = x. With 27 and n = 3 school writes 3, because 3³ = 27. The calculator takes the nth root of x and on these three pairs shows a clean 3, 4 and 3.
16 and 2 are an ordinary square root: 4, because 4² = 16. 81 and 4 give 3, because 3⁴ = 81. Degree n is the second field, not a trick hidden in x.
When n = 0, 1/n does not exist. This implementation does not leave a blank and does not print Infinity: when n is 0 the result is 0, so n = 0 returns 0. That is not ⁿ√x from a notebook, only this code.
A negative x with a non-integer 1/n usually yields a blank value from power. The calculator then clears the result. −27 and 3 will not come back as school −3. A square root of a negative also fails here.
The square-root card next door computes only n = 2 and has its own engine. Here n is a typed field. Floor does not extract a root.
27 and 3 give 3. 16 and 2 give 4. 81 and 4 give 3. n = 0 gives 0.
Formula
n !== 0 ? Math.pow(x, 1/n) : 0
How to use
- Type x and n, for example 27 and 3.
- Click Calculate. The root is 3.
- 16 and 2 give 4. 81 and 4 give 3.
- n = 0 shows 0, because that is how the branch is written, not because ⁰√x = 0 in school.
- A square root alone lives on the square-root card.
27 and 3 give 3
ⁿ√x = power(x, 1/n). 27 and 3 give 3. 16 and 2 give 4. 81 and 4 give 3. n = 0 returns 0.
- root
- A y such that yⁿ = x. 27 and 3 give 3. 16 and 2 give 4.
- Degree
- The second field, n. 4 with 81 gives 3. 0 does not call power, it returns 0.
- power
- The calculator engine. A negative x at 1/3 is usually a blank value and the box stays blank.
Examples
Example 2
- x = 16
- n = 2
4
What is √16? 4. Same square as on the square-root card.
Example 3
- x = 81
- n = 4
3
What is ⁴√81? 3. Three to the fourth is 81.
Related calculators
Common questions
What is ³√27?
3. 3³ = 27. The result is 3.
What does nth root mean?
A y such that yⁿ = x. 16 and 2 give 4. 81 and 4 give 3.
What are √16 and ⁴√81?
4 and 3. The second field is the degree n.
What if n = 0?
When the degree is 0, the result is 0. That is a safeguard in the formula, not the school definition of a root.
Does a negative x work?
Rarely. the cube root of −27 is a blank value, so the result stays blank. School −3 does not come back.
How is this different from the square-root card?
There n is always 2 and the engine is different. Here you type n. 16 and 2 still give 4.
Do 1 and any n give 1?
Yes, when n ≠ 0. 1ⁿ = 1, so ⁿ√1 = 1. n = 0 again returns 0.
Does a comma in 27.0 work?
Yes. 27 and 27.0 at n = 3 give 3.
What about x = 0?
0 when n > 0. Zero to a positive reciprocal power stays zero.
Can the result be a fraction?
Yes. 8 and 2 give about 2.828427, not an integer, because √8 is not 3.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.