# Module 2: Radical Equations and Radical Functions

**Textbook Section 2.1: Graphs of the Square Root Functions**

Textbook Section 2.1: Graphs of the Square Root Functions

**Learning Objectives**

• Graph and compare square root functions.

• Shift graphs of square root functions.

• Graph square root functions using a graphing calculator.

• Solve real-world problems using square root functions.

**Section 2.1 Videos**

**Video Lessons**

- Introduction to Square Root and Perfect Squares
- Graphing the Basic Square Root Function
- Reflections of the Square Root Function
- Horizontal and Vertical Shifts of the Square Root Function
- Horizontal and Vertical Stretches and Compressions of the Square Root Function
- Function Transformation Summary - The Square Root Function

**Video Examples**

**Section 2.2 Textbook: Radical Expressions I**

Section 2.2 Textbook: Radical Expressions I

**Learning objectives**

• Use the product and quotient properties of radicals to simplify radicals.

• Add and subtract radical expressions.

• Solve real-world problems using square root functions.

**Section 2.2 Videos**

**Video Lessons**

**Video Examples**

- Ex: Simplify Square Roots - Perfect Roots
- Ex: Simplify Perfect Nth Roots - Radicals
- Ex: Simplify Square Roots - Not Perfect Roots
- Ex: Simplify a Radical Expression containing Square Roots in the Numerator and Denominator
- Ex: Simplify Radicals with the Same Radicand and Different Indexes
- Ex: Simplify a Radical Containing a Fraction - Perfect Root
- Ex: Simplify Radicals with Variables - Perfect Roots
- Ex: Simplify Radicals Containing Variables With Large Exponents - Not Perfect Roots
- Ex: Simplify Radicals with Negative Radicands and Odd Indexes
- Ex: Simplify Radicals with Variables - Not Perfect Roots
- Evaluating Radical Expressions on the TI83/84
- Ex: Add and Subtract Square Roots - No Simplifying
- Ex: Add and Subtract Square Roots
- Ex: Add and Subtract Square Roots Containing Variables

**Section 2.3 Textbook: Radical Expressions II**

Section 2.3 Textbook: Radical Expressions II

**Learning objectives**

• Multiply radical expressions.

• Rationalize the denominator.

**Section 2.3 Videos**

**Video Lessons**

- Introduction to Multiplying Radicals
- Multiplying Radicals Containing Variables
- Multiplying Binomials with Radicals
- Multiplying Conjugates of Radical Expressions
- Dividing Radicals

**Video Examples**

- Ex: Multiply Square Roots
- Ex 1: Multiply Radicals
- Ex 2: Multiply Radicals
- Ex: Multiply Radicals with Variables
- Ex: Radicals Raised to Powers
- Ex: Distribution with Square Roots
- Ex: Multiply Binomials with Square Roots
- Ex: Square Binomials With Square Roots
- Ex: Multiply Radical Conjugates - Square Roots
- Ex 1: Rationalize the Denominator of a Radical Expression
- Ex 2: Rationalize the Denominator of a Radical Expression
- Ex: Rationalize the Denominator of a Radical Expression - Conjugate

** **

**Section 2.5-2.6 Textbook: The Pythagorean Theorem / Distance Formula / Midpoint**

Section 2.5-2.6 Textbook: The Pythagorean Theorem / Distance Formula / Midpoint

Section 2.5

Section 2.6

**Learning Objectives**

- Use the Pythagorean Theorem.
- Use the converse of the Pythagorean Theorem.
- Solve real-world problems using the Pythagorean Theorem and its converse.
- Find the distance between two points in the coordinate plane.
- Find the missing coordinate of a point given the distance from another known point.
- Find the midpoint of a line segment.
- Solve real-world problems using distance and midpoint formulas.

**Section 2.5-2.6 Videos**

**Video Lessons**

**Video Examples**

- Ex: Determine if a Triangle is a Right Triangle Given the Length of 3 Sides
- Ex: Determine the Length of the Hypotenuse of a Right Triangle
- Ex: Determine the Length of the Leg of a Right Triangle
- Ex: Determine the Distance Between Two Points (length of segment)
- Ex: Midpoint of a Segment

**Section 2.7-2.8 Textbook: Complex Numbers**

Section 2.7-2.8 Textbook: Complex Numbers

Section 2.7

Section 2.8

**Learning Objectives**

- Write square roots with negative radicands in terms of i
- Recognize and write complex numbers in standard form
- Describe the relationship between the sets of integers, rational numbers, real numbers and complex
- numbers
- Add and subtract complex numbers
- Find the complex conjugate of a complex number
- Multiply and divide complex numbers
- Use your calculator to add, subtract, multiply, and divide complex numbers

**Section 2.7-2.8 Videos**

**Video Lessons**

**Video Examples**

- Ex : Simplify Imaginary and Complex Numbers
- Ex: Simplify, Add, and Subtract Imaginary and Complex Numbers
- Ex 1: Adding and Subtracting Complex Numbers
- Ex 2: Adding and Subtracting Complex Numbers
- Ex 1: Simplify and Multiply Complex Numbers
- Ex 2: Multiply Complex Numbers
- Ex 3: Multiply Complex Numbers
- Ex: Multiplying Complex Conjugates
- Ex: Raising the imaginary unit i to powers
- Ex: Dividing Complex Numbers

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