Lesson Map
Use this table as your route through the unit. Lesson numbers jump directly to the matching explanation.
| Lesson | Topic | You should be able to… |
|---|---|---|
| 5.1 | Graphing Irrational Functions | Analyze square-root and related radical graphs. |
| 5.2 | Simplifying Radicals | Simplify radicals and add/subtract like radicals. |
| 5.3 | Multiplying & Dividing Radicals | Multiply radicals and rationalize denominators. |
| 5.4 | Complex Numbers | Use i to represent and calculate with square roots of negative numbers. |
| 5.5 | Rational Exponents | Move between radical notation and rational exponents. |
| 5.6 | Radical Equations | Isolate radicals, raise powers carefully, and check for extraneous solutions. |
| 5.7 | Exponent Applications | Use integer and non-integer exponents in contextual models. |
How the Unit Is Built
Each resource below is part of the same learning cycle. Select a card to jump to it.
Content Summary
Work through these lessons in order. Focus on the meaning of the mathematics, the decision that selects a method, and a check that confirms the result.
Graphing Irrational Functions
Analyze square-root and related radical graphs.
Simplifying Radicals
Simplify radicals and add/subtract like radicals.
Multiplying & Dividing Radicals
Multiply radicals and rationalize denominators.
Complex Numbers
Use i to represent and calculate with square roots of negative numbers.
Rational Exponents
Move between radical notation and rational exponents.
Radical Equations
Isolate radicals, raise powers carefully, and check for extraneous solutions.
Exponent Applications
Use integer and non-integer exponents in contextual models.
Video Library
These links open focused video searches by lesson topic. Use them as reinforcement rather than as a substitute for showing your own reasoning.
Graphing Irrational Functions
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Simplifying Radicals
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Multiplying & Dividing Radicals
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Complex Numbers
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Rational Exponents
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Radical Equations
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Exponent Applications
Use a short lesson after reading the website explanation, then return to the practice.
Find a matching video →Vocabulary
These terms should appear naturally in explanations, diagrams, and written reasoning.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Write a definition in your own words and add an example or sketch in your STRIDES notes.
Sample Problems
Try each problem before opening the solution. The examples are original practice aligned to the unit skills.
Simplify
Show solution
Combine
Show solution
Rationalize
Show solution
Complex number
Show solution
Rational exponent
Show solution
Radical equation
Show solution
Equations & Rules
Know what each relationship means and when it applies; do not treat the box as a list of disconnected formulas.
Review Guide
Skill Checklist
- I can analyze square-root and related radical graphs.
- I can simplify radicals and add/subtract like radicals.
- I can multiply radicals and rationalize denominators.
- I can use i to represent and calculate with square roots of negative numbers.
- I can move between radical notation and rational exponents.
- I can isolate radicals, raise powers carefully, and check for extraneous solutions.
- I can use integer and non-integer exponents in contextual models.
How to review
- Complete the unit Skills Check packet without notes.
- Mark the exact skill behind each error.
- Return to that lesson and complete a fresh example.
- Explain the correction in words, then retry a similar problem.
- Finish with mixed practice so you must choose the method yourself.
Performance Task
Scaling With Non-Integer Exponents
Investigate a physical or geometric relationship involving roots or fractional powers. Build a table, graph the relationship, and explain how the exponent changes growth.
Evidence to include
A labeled mathematical model, organized calculations, appropriate units and precision, a written interpretation, and a check or discussion of limitations.