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Radicals and Radical Equations

Main Topics

  • Simplifying rational expressions (polynomial fractions)

  • Domain restrictions (non-permissible values)

  • Operations with rational expressions (+ − × ÷)

  • Least common denominator (LCD) and simplification

  • Solving rational equations and checking for extraneous solutions

  • Applications in rates, proportions, and work problems

Key Skills

  • Simplify and combine rational fractions accurately

  • State restrictions and justify solutions

  • Apply algebraic reasoning to rational situations

  • Solve real-world ratio and rate problems


This unit expands on earlier radical concepts by introducing equations that contain radicals. Students learn how to isolate radicals, square both sides properly, and check for extraneous solutions. They also study how to represent and transform radical functions on graphs. This topic helps students visualize non-linear growth patterns and understand how radicals connect algebraically to powers and roots.

Summmary

Suggested Activities

  • LCD practice sets

  • Word problems involving rates and work

  • Rational equation challenge quiz

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