Root Calculator
Our free arithmetic calculator solves root problems. Get worked examples, visual aids, and downloadable results. Enter your values for instant results.
Formula
n-th root of x = x^(1/n)
The nth root of a number x is a value r where r^n = x. It is equivalent to raising x to the power 1/n. For n = 2 (square root), n = 3 (cube root), and so on. Even roots of negative numbers are not real; odd roots of negative numbers are negative real numbers.
Worked Examples
Example 1: Cube Root of 27
Problem: Calculate the cube root of 27 and verify the result.
Solution: Cube root of 27 = 27^(1/3) = 3\nVerification: 3^3 = 3 x 3 x 3 = 27\n27 = 3^3, so this is a perfect cube.\nAs exponent form: 27^(1/3) = 27^0.333333
Result: The cube root of 27 is exactly 3, a perfect cube.
Example 2: Fourth Root of 625
Problem: Find the fourth root of 625.
Solution: Fourth root of 625 = 625^(1/4)\n625 = 5^4 = 5 x 5 x 5 x 5\nSo 625^(1/4) = 5\nVerification: 5^4 = 625\nAlternatively: sqrt(sqrt(625)) = sqrt(25) = 5
Result: The fourth root of 625 is exactly 5.
Frequently Asked Questions
What is a root in mathematics?
A root (or radical) is the inverse operation of exponentiation. The nth root of a number x is a value r such that r raised to the nth power equals x. The most common root is the square root (n = 2), which asks what number multiplied by itself gives x. For example, the square root of 25 is 5 because 5 times 5 equals 25. The cube root (n = 3) asks what number cubed gives x: the cube root of 8 is 2 because 2 times 2 times 2 equals 8. Roots can be expressed using radical notation or as fractional exponents, where the nth root of x equals x raised to the power 1/n.
What formula does Root Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.
Can I use Root Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
Does Root Calculator work offline?
Once the page is loaded, the calculation logic runs entirely in your browser. If you have already opened the page, most calculators will continue to work even if your internet connection is lost, since no server requests are needed for computation.
How accurate are the results from Root Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.