Root Calculator
Our free arithmetic calculator solves root problems. Get worked examples, visual aids, and downloadable results. Enter your values for instant results.
Reviewed by Manoj Kumar, Mathematics Educator
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.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy