How to calculate an nth root
The n-th root of x is the number that, when raised to the power n, equals x: x^(1/n). For example, the 5th root of 32 is 2 because 2⁵ = 32, and the 4th root of 81 is 3 because 3⁴ = 81. For n = 2 the familiar shortcut is the square root calculator.
Square roots, cube roots and beyond
Set n = 2 for a square root and n = 3 for a cube root — or jump straight to the cube root calculator. Any positive integer n works here, so you can compute 4th, 5th or higher roots in one step.
- Larger n pulls results toward 1. The 10th root of 32 is about 1.41, while the 5th root is 2.
- Roots of numbers below 1 grow. The square root of 0.25 is 0.5, which is larger than the input.
- Most roots are irrational, so the displayed value is rounded rather than exact.
Negative numbers and even roots
Odd roots (n = 3, 5, 7…) of negative numbers are real, for example the cube root of −8 is −2. Even roots (n = 2, 4…) of negative numbers have no real value, so the calculator reports "no real root" in that case. Every root is a fractional power, so the exponent calculator gives the same answers written differently.
Frequently asked questions
- What is the 5th root of 32?
- The 5th root of 32 is 2, because 2 × 2 × 2 × 2 × 2 = 32.
- How do I find a square root with this tool?
- Enter your number and set the root index n to 2. The result is the square root.
- Can I take an even root of a negative number?
- No real value exists for an even root of a negative number, so the calculator shows "no real root."
- What does x^(1/n) mean?
- Raising x to the power 1/n is the same as taking the n-th root of x.
- Can the root index be a fraction or a negative number?
- Yes, and both are meaningful. A root index of 0.5 is the same as squaring, since x^(1/0.5) = x². A negative index gives the reciprocal of the ordinary root, so the −2nd root of 16 is 1 ÷ 4 = 0.25. Only n = 0 is undefined.