Mathematics · Grade 11 · Algebra 2
Rational Radical Equations and Valid Solutions
Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs.
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Learning goals
- Record domains before algebraic transformations.
- Find candidates and check original equations.
- Explain extraneous roots and excluded inputs.
Before you begin
Factor quadratics, solve linear equations and interpret principal square roots.
Age and grade do not measure readiness. Adjust reading or adult support to preserve the intended learning goal.
Follow the sequence
Complete practice
Rational Radical Equations and Valid Solutions
Practice · Independent · 45 min
Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.
1. Explore
Rational Radical Equations and Valid Solutions: Explore and Explain
Explore · Independent · 12 min
Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.
2. Practice
Rational Radical Equations and Valid Solutions: Practice Independently
Practice · Independent · 20 min
Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.
3. Apply
Rational Radical Equations and Valid Solutions: Apply and Create
Apply · Independent · 25 min
Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.
Teaching and response guide
- Begin with: What restriction follows because the square root must equal a nonnegative right side?
- Connect the response to: List all roots of that quadratic.
- Ask students to apply the idea: Explain why squaring made x = 0 appear as a candidate although it fails the original equation.
Watch for: An algebraic candidate is not a solution until it satisfies the original domain and equation.
Check the answer criteria for each task. A supported explanation may have more than one acceptable response. These activities offer evidence to discuss; completing a sheet alone does not establish mastery.
Possible next goals
Choose the next unit when its prerequisites fit your learner.