Root Calculator
Calculate the nth root of any number. Enter the radicand and root degree to get the exact radical value, power function chart, and step-by-step breakdown.
About This Calculator
The Root Calculator computes the nth root of any positive or negative number with high decimal precision. Whether you need a square root (n=2), cube root (n=3), fourth root, or any higher-order radical, this tool provides the exact value using the formula nsqrtx = x^(1/n). Simply enter the radicand and the root degree, and the calculator returns the result instantly along with a breakdown and a power function chart.
The nth root operation is the inverse of exponentiation: if bⁿ = a, then b is the nth root of a. The calculation uses exponentiation under the hood -- Math.pow(a, 1/n) -- giving precise results for any real radicand as long as the root is odd for negative inputs. This calculator is ideal for students learning radicals, engineers working with formulas, and anyone who needs quick root computations without a scientific calculator.
Regional Notes
India (IN): Radicals and surds are taught extensively in CBSE and state board curricula from Class 8 onward. Students preparing for competitive exams like JEE, NEET, and SSC will find this nth root calculator useful for quickly evaluating roots during practice.
United States (US): The Common Core standards cover radicals under the Number and Quantity domain (HSN-RN). This calculator helps high school and college students verify their work with square roots, cube roots, and higher radicals in algebra and precalculus courses.
United Kingdom (UK): The GCSE and A-Level mathematics curricula include surds, indices, and radical expressions. Students can use this tool to check their manual calculations when simplifying expressions involving nth roots.
Frequently Asked Questions
What is an nth root in mathematics?
The nth root of a number x is the number that when raised to the power n gives x. It is written as the radical symbol with an index n: nsqrtx. For example, the cube root of 8 is 2 because 2^3 = 8.
How do you calculate the nth root of a number?
The nth root of a number a is calculated as a^(1/n). For perfect powers the result is an integer, and for non-perfect powers the calculator returns a decimal approximation. The calculator handles positive and negative numbers -- for negative radicands, the root must be odd.
What is the difference between square root and cube root?
A square root (n=2) finds a number that when multiplied by itself gives the original. A cube root (n=3) finds a number that when cubed gives the original. Square roots of negative numbers are not real, while cube roots of negative numbers are real and negative.
Can you take the nth root of a negative number?
You can take an odd root (cube root, fifth root, etc.) of a negative number and get a real negative result. However, even roots (square root, fourth root) of negative numbers produce imaginary results, which are not supported by this calculator.
What is the fourth root of 81?
The fourth root of 81 is 3, because 3^4 = 3 x 3 x 3 x 3 = 81. This calculator can find any nth root, from square roots to higher-order radicals like the 10th root.
How do nth roots relate to fractional exponents?
The nth root of a number is equivalent to raising that number to the power of 1/n. For example, the cube root of 8 can be written as 8^(1/3), and both equal 2. Fractional exponents follow the same rules as integer exponents.
What is the nth root of 1?
The nth root of 1 is always 1 for any positive integer n, because 1 raised to any power equals 1. This is true for all real roots.