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.