Radical
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. 

Note. 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.
Surd
A radical expression that is left as is and not evaluated is called a surd. See definition of surd.
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Other exponents and roots topics
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