Which step is necessary when working with surds in the denominator of an expression?

When working with surds in the denominator of an expression, rationalizing the denominator is a necessary step. The purpose of this process is to eliminate the surd from the denominator, making the expression easier to work with and simplifying calculations. This is typically done by multiplying the numerator and the denominator by a suitable form of the surd, which transforms the denominator into a rational number.

For example, if you have an expression like ( \frac{1}{\sqrt{2}} ), rationalizing the denominator would involve multiplying both the top and bottom by ( \sqrt{2} ). This results in ( \frac{\sqrt{2}}{2} ), where the denominator no longer includes a surd, simplifying further computations and interpretations of the expression.

In contrast, steps such as finding a common factor or converting to standard form do not directly address the issue of surds in the denominator. Solving for x typically pertains to equations rather than simplifications of fractions involving surds. Thus, rationalizing the denominator is the key step needed in this context.