Math Exponents and roots Roots

nth root

The inverse of exponentiation is the root of a number. The base is determined with the exponent and the exponentiation value.

$\color{red}{x}^n=a\Leftrightarrow \color{red}{x} = \sqrt[n]{a}$

$x ...$ the base
$n ...$ the exponent
$a ...$ the exponentiation value or rather radicand as you are watching at the radical symbol.

Example: $4\cdot4=16$ and the square root of $16$ is: $\sqrt[2]{16}=4$



Square roots are roots whose exponent is 2. You do not have to write this one: $\sqrt[2]{a}=\sqrt{a}$


Square roots can only be taken from positive numbers. The radicand must not be negative.


  • $\sqrt[3]{8}=2$, because $2^3=8$
  • $\sqrt{36}=6$, because $6^2=36$
  • $\sqrt{-25}=\text{not defined}$