# What is the sqrt(-25)?

$\sqrt{- 25} = 5 i$
$- 25$ has two square roots $5 i$ and $- 5 i$, but the expression $\sqrt{- 25}$ denotes the principal square root, which by convention is $5 i$.
In general, if $x < 0$ then $\sqrt{x} = \left(\sqrt{- x}\right) i$. Hence in our example:
$\sqrt{- 25} = \left(\sqrt{25}\right) i = \left(\sqrt{{5}^{2}}\right) i = 5 i$