nth Root Calculator

The nth root calculator finds the principal root of any number for any root index you choose. A root is the inverse of exponentiation: the nth root of a number x is the value that, when multiplied by itself n times, gives back x. The square root is the 2nd root, the cube root is the 3rd root, and you can go as high as you like with 4th, 5th, or higher roots. The formula is straightforward: the nth root of x equals x raised to the power of one over n, written as x^(1/n). You enter two values: the root index n (which must be a positive integer) and the radicand, which is the number you want to find the root of. The calculator returns the principal root rounded to six decimal places, a verification figure showing what happens when you raise the result back to the power n (which should match your original radicand), and a written description of the operation. For odd-indexed roots of negative numbers, the real root exists and is negative. For even-indexed roots of negative numbers, the result is complex and the calculator will tell you so rather than returning an error silently. The tool is useful for students working through algebra, calculus, or physics problems, for engineers converting between power laws, and for anyone who needs a fast, reliable check of a root calculation. Results are mathematical values and carry no rounding guarantee beyond six decimal places.

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