Root Calculator

Calculate square roots, cube roots, and any nth root of a number instantly.

Calculate square roots, cube roots, and Nth roots.

Number (x)

Root (n)

Nth Root Formula

The n^th root of x is a number r such that rⁿ = x.

Understanding the Root Calculator

Calculate square roots, cube roots, and general N-th roots of any number. visualize the root function curve.

Guide

1Enter the 'Number' (radicand) you want to find the root of.
2Enter the 'Root' index (n). Use 2 for Square Root, 3 for Cube Root.
3The result will show the value. If it's an even root of a negative number, it will indicate it's imaginary/complex.
4View the graph to see how the root function behaves.

Applications

Geometry: Finding the side length of a square from its area (Square Root).

Physics: Calculating Root Mean Square (RMS) values.

Finance: Calculating Compound Annual Growth Rate (CAGR).

Volume: Finding side length of a cube from its volume (Cube Root).

r = x^(1/n)

The n-th root of a number x is a number r which, when raised to the power n, yields x. This is equivalent to raising x to the power of (1/n).

Knowledge Base

In the real number system, it's undefined. In the complex number system, it involves 'i' (the imaginary unit).

The cube root of a number is a value that, when multiplied by itself three times, gives the original number.

Yes! But usually we talk about 'fractional exponents'. A root index of 0.5 is actually squaring the number (x^(1/0.5) = x^2).

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