Root Calculator

Calculate square root ($\sqrt{x}$), cube root ($\sqrt[3]{x}$), or any $n^{\text{th}}$ root ($\sqrt[n]{x}$) instantly.

General $n^{\text{th}}$ Root Calculator

Calculate $\sqrt[n]{x}$ for any degree $n$ and radicand $x$.

Root Degree ($n$):

Radicand Value ($x$):

A root of a number $x$ is another number that, when multiplied by itself $n$ times, gives $x$.

$n^{\text{th}}$ Root Exponent Form: \sqrt[n]{x} = x^{(1/n)}

Product Rule for Radicals: \sqrt[n]{a \times b} = \sqrt[n]{a} \times \sqrt[n]{b}

Quotient Rule for Radicals: \sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}

In real number arithmetic, negative numbers do not have real square roots. However, in complex mathematics, $\sqrt{-1} = i$ (an imaginary number).

Yes, odd degree roots (like cube roots $\sqrt[3]{-27} = -3$) are well-defined for negative real numbers.

An nth root is a value that, when multiplied by itself n times, equals the original number. Square roots and cube roots are common examples.

Yes. It supports square roots, cube roots, and general nth roots for valid numeric inputs.

Root calculations are widely used in algebra, geometry, engineering, physics, finance, statistics, and computer science.