The bar length matters

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.

Used in a radical expression

The three components of a radical expression are

Degree	The number of times the radicand is multiplied by itself. 2 means square root, 3 means cube root. After that they are called the 4th root, 5th root and so on. If this is missing, it is assumed to be 2 - the square root.
Radical symbol	The √ symbol that means "root of". The length of the horizontal bar is important. See note below.
Radicand	The thing you are finding the root of.