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.