# How do you simplify sqrt(-52) ?

The number $\sqrt{- 52}$ is a pure imaginary number.
It may be written as $\sqrt{52} . \sqrt{- 1}$ .
Now writing $\sqrt{- 1} = i$, $\implies \sqrt{- 52} = \sqrt{52} i$ .
Now, $52 = 13 \cdot 4$, thus $\sqrt{- 52} = \sqrt{13 \cdot 4} i = 2 \sqrt{13} i$.