Strolling in the Cartesian plane

Suppose you are standing at the coordinates $(0,0)$ . You have been instructed to move to the coordinates $(a,b)$ , but instead you move to the coordinates $(b,a)$ . How far are you from your destination?

The distance can be expressed as $|a-b| \sqrt c$ (here, $a$ and $b$ are the same as used above and $c$ is square-free).

What is the value of $c$ ?

$\text{Note:} a\neq b$