What is the main purpose of rationalizing a denominator in a mathematical expression?

Rationalizing a denominator primarily involves eliminating radicals from the denominator. This process is undertaken because having a radical in the denominator can complicate both the interpretation and manipulation of a mathematical expression. By rationalizing the denominator, you convert the expression into a form that is easier to work with, especially in further calculations or when combining fractions.

For example, if you have a fraction like (\frac{1}{\sqrt{2}}), rationalizing it by multiplying both the numerator and denominator by (\sqrt{2}) yields (\frac{\sqrt{2}}{2}). This expression is often more straightforward to handle in subsequent computations compared to one with a radical in the denominator.

While simplifying calculations and making an expression look neater can be benefits of rationalization, the fundamental goal is the removal of the radical, which enhances clarity and usability in mathematical processes. Converting to an improper fraction does not relate to the rationalization of denominators and serves another purpose in fraction manipulation.