Performing arithmetic with radical expressions is one of those summary tasks pulling together a surprising number of subskills. Learners need to simplify radicals, identify common radicands, perform FOIL, along with applying arithmetic methods appropriately inside and outside radicands. This approachable presentation demonstrates and explains examples of all of these arithmetic skills, starting with the simplest of adding problems then scaffolding through the more complex examples of FOIL and simplification. A great addition to your existing radical expression arithmetic curriculum to introduce or review these key skills.

CCSS: Designed
##### Instructional Ideas
• Consider linking on a class website for pre-class viewing in the flipped classroom model, or for individual on-demand remediation after covered in class
• A useful application of radical arithmetic involves finding perimeters and areas of composite shapes that include right triangles and require applying the Pythagorean Theorem
• Linking with a physics curriculum around combining forces through vector addition or voltage formulas provides real-life examples of manipulating radical expressions
##### Classroom Considerations
• Simplifying radicals is shown by dividing out the largest square rather than prime factorization methods
• Video requires Internet access
• Radicals shown are all square roots, no higher order roots
• Consider pausing the presentation between examples to allow pupils time to figure out problems themselves
• This resource is only available on an unencrypted HTTP website. It should be fine for general use, but don’t use it to share any personally identifiable information
##### Pros
• Pleasant and easily understood narration
• Example problems start simple and increase logically in difficulty
• Each problem is explained step by step and worked thoroughly from start to finish
• The numbers chosen for each example emphasize potential complications and allow for explanation of pitfalls without becoming overly cumbersome
##### Cons
• No printable notes or individual slides for notetaking provided
• No available seatwork or guided practice problems to match the presentation