The horizontal bar in the radical symbol tells how much of the expression is to be used.
In this expression: the bar stretches across the whole expression "p - q". So this means we subtract q from p, then find the square root of the result.
If it has only covered the 'p' like this: it would mean find the square root of p then subtract q from the result.
The bar acts like parentheses, telling you how to group items and the order of calculation.
The radical sign is a symbol that means "root of". The length of the horizontal bar is important. See note below. When used in an expression like the one above, the whole expression is called a radical.
The three components of a radical expression are