# Definition:Square Root/Negative Real

## Definition

Let $x \in \R_{< 0}$ be a (strictly) negative real number.

Then the square root of $x$ is defined as:

$\sqrt x = i \paren {\pm \sqrt {-x} }$

where $i$ is the imaginary unit:

$i^2 = -1$

Hence:

$\sqrt{-1} = i$