We are asked to complete the following sentence.

You $\underline{?}$ of a radical expression by rewriting it without radicals in the denominator.

The fact that the sentence begins with you suggests that we should complete it with a verb. We need to think of a name for the process of rewriting a radical expression without radicals in the denominator. First, let's recall what a radical expression is.

53, 812, 11

The thing that all these expressions have in common is a radical. That is why they are called radical expressions. They can also have radicals in the denominators. Here are a few examples.

\frac{7}{2}, \frac{2}{3 5}, \frac{1 3}{3}

Because they have radicals in the denominators, these are not rational expressions. What would happen if we got rid of the radicals in the denominators? Let's try! To do so, we need to multiply each fraction by another fraction. This fraction will have both the numerator and the denominator equal to the radical of our fraction.

Radical Expression	$\frac{7}{2}$	$\frac{2}{3 5}$	$\frac{1 3}{3}$
Multiply	$\frac{7}{2} \cdot \frac{2}{2}$	$\frac{2}{3 5} \cdot \frac{5}{5}$	$\frac{1 3}{3} \cdot \frac{3}{3}$
Simplify	$\frac{7 2}{2}$	$\frac{2 5}{3 \cdot 5}$	$\frac{1 3 3}{3}$
Final Expression	$\frac{7 2}{2}$	$\frac{2 5}{1 5}$	$\frac{3 9}{3}$

Now each expression has a rational number in the denominator. Therefore, we rationalized the denominators of the radical expressions. Let's complete the given sentence.

You $\underline{rationalize the denominator}$ of a radical expression by rewriting it without radicals in the denominator.

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