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: $\sqrt[2]{16}=4$
i
Information
Square roots are roots whose exponent is 2. You do not have to write this one: $\sqrt[2]{a}=\sqrt{a}$
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Remember
Square roots can only be taken from positive numbers. The radicand must not be negative.
Examples
- $\sqrt[3]{8}=2$, because $2^3=8$
- $\sqrt{36}=6$, because $6^2=36$
- $\sqrt{-25}=\text{not defined}$