Radical Functions Task Cards

Radical functions are usually taught in the second semester of Algebra 2, and I find that students struggle with understanding the different operations and properties of radicals. My differentiated radical functions task cards make it easy to provide extra practice that meets students at their level! Students gain knowledge and confidence as they work through these topics. Read on to discover how each topic is broken down into easy, medium and hard task cards, available for sale in my TpT store.

Want a FREE set of differentiated task cards? CLICK HERE!

Simplifying Radical Expressions

The first thing students need to know when working with radicals is how to simplify a single radical expression, including higher order radicals such as cube roots and fourth roots. All of the other principles will follow from a solid understanding of how a radical really works. I would even spend an extra day on simplification if needed, just to be sure that students are ready to perform other operations on radicals! The task cards I created for simplifying radicals break down into three categories.

Easy: Simplifying a square root with one coefficient and one variable under the radical. None of the radicals have a coefficient outside the radical.
Medium: Simplifying a square root with a coefficient outside the radical and two variables underneath the radical.
Hard: Simplifying a cube root with a coefficient outside the radical and two variables underneath the radical.

Adding and Subtracting Higher Order Radical Expressions

After teaching simplifying radicals, I revisit adding and subtracting. Because students have had practice with adding and subtracting square roots, this should be a skill that builds upon their previous knowledge. These task cards break down into three levels:

Easy: Adding or subtracting square roots only
Medium: Adding or subtracting radicals with higher indices (cube root, fourth root). The problems only have two terms.
Hard: Adding or subtracting expressions with higher indices and more than two terms.

Multiply Radical Expressions

Once students know how to add and subtract I move on to multiplication.

Easy: Two square roots, some with coefficients, multiplied together.
Medium: A radical term distributed over a binomial.
Hard: Two binomials multiplied together.

Dividing Radical Expressions

Dividing radical expressions needs to come last because students need to know how to multiply in order to rationalize the denominator.

Easy: Square root expressions divided by square root expressions. The expression may need to be simplified before rationalizing.
Medium: A single radical divided by a binomial that contains radicals.
Hard: A binomial divided by a binomial that contains radicals.