These 18 task cards are a great way to challenge your Algebra students and test their proficiency in rationalizing the denominator or numerator of radical expressions. Students should know how to find the conjugate of a rational expression with two terms.

Suggested use of task cards: Print one set of task cards. Pair students together and set up a rotation so that each pair knows who they will hand off their task card to. Give each pair a task card and each student should have his/her own recording sheet to show work and record their answers. Time the students (two to three minutes) and then have them switch the card by passing it to another pair of students in the rotation. With 18 task cards (unless you have a class of 36 or more), you’ll have task cards left over. I usually give the first group a task card from my pile of left-overs and then collect the last task card from the last group in the rotation so that the students don’t have to constantly get up from their seats. This will vary depending on your class size, seating arrangements, class configuration, etc.

You can also print a set per small group (of 3 or 4 students) and have them go through the task cards together. It’s completely up to you.

Objectives: Students will be able to
• Use the product rule for radicals
• Use the quotient rule for radicals
• Simplify radicals
• Rationalize denominators
• Rationalize denominators having two terms
• Rationalize numerators

Common Core Standards
• Expressions and Equations Work with radicals and integer exponents.
o CCSS.Math.Content.8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.
o CCSS.Math.Content.8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.