How do you simplify radical expressions?
There are two common ways to simplify radical expressions, depending on the denominator.
Using the identities
Case 1: the denominator consists of a single root. For example, let's say that our fraction is
Case 2: the denominator consists of a sum/difference of roots. If we multiply by the difference/sum of the roots, we'll have the same result as above. For example, if you have
You'll multiply numerator and denominator by the difference
which finally equals
Of course, when working with radicals, you always need to pay attention and make sure that the argument of the root is positive, otherwise you will write things that have no meaning!