Conjugate Theorem
One of the “rules” for simplifying radicals is that you should never leave a radical in the denominator of a fraction. The way to get rid of a square root is to multiply it by itself, which of course will give you whatever it was the square root of. To keep things legal, you must do to the numerator whatever you do to the denominator, and so we have the rule.
Read more about the conjugate theorem below.
Practice: Use the identity of the difference of two squares to have no radicals in the denominators in the following exercises.