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Algebra I Lesson

Radical Operations: Combining, Multiplying, and Rationalizing

Shared by A STEM Educator

8th or 9th GradeBuilding Thinking Classrooms (BTC)CCSS.MATH.CONTENT.HSN.RN.A.2, CCSS.MATH.CONTENT.HSN.RN.B.360 min
Learning Objective

Students will simplify radicals, add and subtract like radicals, multiply radical expressions using the distributive property, and rationalize denominators containing both monomial and binomial radical expressions.

Lesson Overview

Students discover the structural rules of radical arithmetic by analogy to polynomial operations, then progressively master simplifying, combining, multiplying, and rationalizing radicals — culminating in conjugate rationalization and complex rectangle problems.

Materials

  • Vertical non-permanent surfaces (whiteboards) or chart paper
  • Dry-erase markers (one per group)
  • Erasers or paper towels
  • Visibly random grouping cards
  • Printed or projected warm-up columns
  • Exit slip half-sheets

Scaffolded Task Progression

1Task 1
Calculate the exact perimeter of a triangle with side lengths , , and . (Hint: At first glance, none of the radicands match! What must you do to all three radicals first before you can combine them?)
2Task 2
Multiply . Multiply the outside coefficients together and the inside radicands together. Simplify your final radical completely.

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