Nth Root Calculator
Find any root of a number — square, cube or nth.
Results update as you type.
How it works
The nth root of a number is the value that produces that number when multiplied by itself n times, and this calculator finds any root you need, from the familiar square and cube roots to any higher degree. You enter the number and the root degree, and it returns the result, computing the root as the number raised to the power of one divided by the degree. The square root, degree two, asks what number squared gives your value; the cube root, degree three, asks what number cubed does. Roots are the inverse of powers and appear constantly in mathematics, geometry, finance, and science, from computing side lengths and standard deviations to finding growth rates and solving equations. This calculator correctly handles odd roots of negative numbers, such as the cube root of negative eight being negative two, because a negative number raised to an odd power stays negative. It returns no real result for even roots of negatives, like the square root of negative four, since no real number squared is negative; those require complex numbers. You can also use non-integer degrees for fractional roots. Enter the number and the root degree to compute the root.
ⁿ√x = x^(1/n)
The nth root of a number x is the value that, raised to the power n, gives back x, which is the same as raising x to the power one over n. The square root uses n equal to two and the cube root uses three. Negative numbers have a real root only when n is an odd whole number.
Source:Algebra
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter number and root degree (n).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Result updates instantly as you type — no button to press.
Frequently asked questions
What is an nth root?
The nth root of a number is the value that, when raised to the power n, returns the original number. The second root is the square root and the third is the cube root. Finding the nth root is the same as raising the number to the power of one divided by n, which is how this calculator computes it.
Can you take the root of a negative number?
You can take an odd root of a negative number and get a real result: the cube root of negative eight is negative two, since negative two cubed is negative eight. Even roots of negatives, such as the square root of negative four, have no real value because no real number squared is negative; they require complex numbers.
How is the nth root related to exponents?
Taking the nth root is exactly the same as raising a number to the fractional power one over n. So the cube root of eight equals eight to the power one third, which is two. This relationship lets calculators and computers evaluate any root using exponentiation, and it underlies the laws of exponents for fractional powers.
Can the root degree be a decimal?
Yes. The degree does not have to be a whole number. A degree of 2.5, for instance, computes the 2.5th root, equal to raising the number to the power of one divided by 2.5. Fractional degrees are meaningful for positive numbers; for negatives, only odd whole-number degrees give a real result.
What is the difference between a root and a power?
A power multiplies a number by itself a given number of times, while a root reverses that operation, asking which number was multiplied to reach a value. They are inverse operations: raising to the power n and taking the nth root undo each other. Roots are written as fractional exponents, tying the two ideas together.