An expression that uses a root, such as square root, cube root. See definition of root.

The three components of a radical expression are


The thing you are finding the root of.

Radical symbol

The symbol that means "root of". The length of the horizontal bar is important. See note below.


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.

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.


A radical expression that is left as is and not evaluated is called a surd. See definition of surd.

Other exponents and roots topics