Radical sign or symbol
A symbol √ used to indicate that a root is being taken  such as a square root.
See definition of root.
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. 

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