About Nth Root Calculator
This nth root calculator finds the number that, raised to the power n, gives yours. It works for any whole index from 2 to 100 and simplifies the radical. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on the 4th root of 800. Since 800 = 2⁵ × 5², four 2s make one group and come out, leaving 2 × 5² under the root: 24√50, about 5.318296.
The nth root is the same as raising to the power 1/n, so the 5th root of 32 is 32^(1/5) = 2. For even n the root of a negative number is not real, and for odd n it is.
How to use Nth Root Calculator
- Choose Square root, Cube root, nth root or Simplify radical.
- Type the number. A whole number, a decimal or a fraction all work, and negatives are allowed.
- For an nth root, type the root index. Choose how many decimal places you want.
- Read the exact form and the decimal at the top.
- Open the steps to see the prime factorization and the pairs taken out of the root.
Features
- Simplified radical form with the prime factorization shown: √72 = 6√2.
- Decimal to up to 100 places, computed exactly with integers.
- Square roots, cube roots and nth roots up to index 100.
- Imaginary results for negative numbers under even roots, and real roots for odd ones.
- Perfect squares and perfect powers are recognised and shown exactly.
- Decimals and fractions accepted, with the denominator rationalised.
- Step-by-step working in KaTeX and a copy button.
The nth root
The nth root is a fractional power.
ⁿ√x = x^(1/n)
ⁿ√(aⁿb) = a · ⁿ√bWorked examples
4th root of 800 gives 24√50 ≈ 5.318296
800 = 2⁵ × 5².
5th root of 243 gives 3
3⁵ = 243, so it is a perfect fifth power.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- To estimate a square root by hand, find the two perfect squares around it. √50 is between √49 = 7 and √64 = 8, so it is a little over 7.
- A decimal that neither ends nor repeats means the root is irrational, which is true of the root of any number that is not a perfect power.
- Check a decimal root by squaring it. The result should be very close to the number you started with.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I find the nth root of a number?
Raise the number to the power 1/n. By hand, factor it into primes and take out every prime that appears n times.
Is the nth root the same as a fractional exponent?
Yes. The nth root of x is x^(1/n), so the cube root of x is x^(1/3).
More Square Root Calculator pages
- Square Root CalculatorEnter a number to get its square root in simplest radical form and as a decimal, with the working.
- Cube Root CalculatorEnter a number to get its cube root, exact where possible, with the working.
- Simplify Radical CalculatorEnter the number under the root and get the radical in simplest form with the steps.
- Square Root of 2The square root of 2 is about 1.41421356, and its digits never end or repeat.
- Square Root of 3The square root of 3 is about 1.7320508, and its digits never end or repeat.
- Square Root of 72The square root of 72 simplifies to 6√2, which is about 8.4853.