In these worksheets, students will learn to rationalize denominators with radicals.

#### Imagine having fun solving math questions, and then there are radicals, uh! What a struggle. We will not lie, radicals scare each and every one of us, especially when they appear in the denominator of a fraction. Thankfully, there is a way we can remove radicals from the denominator. So, how do we do that? SIMPLE! We rationalize. Now, what is rationalizing? When solving radicals, we know that multiplying two same radicals, cancels out the radical, ow awesome? Now, we use this technique to address the radicals in the denominators. Consider, you have a fraction with a radical in its denominator. 1/√2.What you need to do is, multiply both numerator and the denominator with the radical. And it becomes; 1 / √2 × √2 / √2 = √2/ 2. This is what needs to be done; this is the case when you have a single radical in the denominator. What if you have an expression containing a radical in the denominator. What you need to do then? To go further, you need to understand what is a conjugate as we will use this in the rationalizing procedure. Conjugate is when the sign between two terms in an expression is changed. If you have an expression; 3-√2 and its conjugate will be 3+√2. Consider a fraction; 1/(3-√2) × (3+√2) / (3+√2) = (3+√2) / (9-2) = (3+√2) / 7.

Rationalizing denominators is the process of rewriting a fraction so that the denominator contains only rational numbers. A radical expression is an expression containing a radical (v) (sometimes also called a square root) symbol. In many of these problems, the radicals are in the denominators. Students will rewrite expressions so that the radical in each expression is in the numerator. Students will also simplify fractions that contain a radical in either the numerator or the denominator. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. There are also worksheets provided for students to use to practice independently. When finished with this set of worksheets, students will be able to rewrite expressions so that there is no radical in the denominator, and simplify fractions containing radicals. These worksheets explain how to rationalize denominators with radicals. Sample problems are solved and practice problems are provided.

# Rationalizing Denominators with Radicals Worksheets

## Lesson

This worksheet explains how to rationalize denominators the expression: 4 / √3. The sample problem is solved and two practice problems are provided.

## Rationalizing Denominators with Radicals Worksheet

A really nice mix of problems where you may: rationalize denominators, simplify values, or write equivalent expressions. Ten problems are provided.

## Practice

Students will practice rationalizing denominators and evaluate a slew of radicals. Ten problems are provided.

## Review

The concept of how to rationalize denominators with radicals is reviewed. A sample problem is solved and six practice problems are provided.

## Quiz

Students will demonstrate their proficiency with this skill on this quiz. Ten problems are provided.

## Check

This is a great way to introduce or review this skill. Three problems are provided, and space is included for students to copy the correct answer when given.