A radical expression is a numerical expression or an algebraic expression that include a radical.
See below 2 examples of radical expressions.
Notice also that radical expressions can also have fractions as expressions.
There are 3 important pieces of information in any radical expressions that are important to identify. These are the radical sign, the radicand, and the index.
Take a look at the following radical expression.
What if the index is n? Then the expression below means that we are looking for the nth root.
If the index n is even, the radicand a must be nonnegative for the root to be a real number.For example, the following radical expressions do not have a real number root because the indices are 4 and 2 and these are even numbers.
If the index n is an odd number, then the radicand do not have to be nonnegative for the root to be a real number.
For example, the following radical expressions still have a real number root since the indices 3 and 5 are odd numbers.
The following radical expressions have algebraic expressions as radicands.
The following radical expressions have numerical expressions as radicands.