# Ch 4: CAHSEE - Problems with Radical Expressions & Equations: Tutoring Solution

### About This Chapter

## How it works:

- Begin your CAHSEE math exam preparation.
- Identify the radical expressions and equations concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our CAHSEE Tutoring Solution will benefit any student who is trying to learn about radical expressions and equations and earn passing scores on the exam. This resource can help students including those who:

- Struggle with understanding complex expressions, radical notation, square roots or any other radical expressions and equations topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning about math visually
- Find themselves struggling with preparation for the CAHSEE math exam
- Cope with ADD or ADHD
- Want to get ahead in high school math
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning about radical expressions and equations simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live math tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about radical expressions and equations on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Learn how to estimate square roots.
- Evaluate the square roots of perfect squares.
- Simplify square roots that are not a perfect square.
- Understand how to simplify complex expressions that include square roots.
- Be able to simplify the square roots of quotients.
- Rationalize the denominators of radical expressions.
- Add and subtract using radical notation.
- Multiply radical expressions that contain two or more terms.
- Solve radical equations.
- Explain how to solve radical equations that have two radical terms.

### 1. Estimating Square Roots

Inverse operations are mathematical operations that undo each other. The square root is the inverse of the squared (or multiplying a number by itself) operation. There is an easy method for estimating the square root of a number, which you will learn in this lesson.

### 2. Evaluating Square Roots of Perfect Squares

Squares and square roots are inverse, or opposite, operations involving radicals. Learn how to determine the square root of perfect squares in this lesson.

### 3. Simplifying Square Roots When not a Perfect Square

Numbers that are imperfect squares are those that, when evaluated, do not give solutions that are integers. The proper mathematical way to simplify these imperfect squares is discussed in this lesson.

### 4. Simplifying Expressions Containing Square Roots

In order to write radical expressions correctly, they have to be written in their simplest form. This lesson will show you how to simplify expressions containing numbers and variables inside a square root.

### 5. Simplify Square Roots of Quotients

The quotient rule can be used to simplify square roots of quotients. This lesson will define the quotient rule and show you how it is used to simplify square roots.

### 6. Rationalizing Denominators in Radical Expressions

Radical expressions containing denominators are not simplified completely unless the denominator is free of radical symbols. This lesson will teach you how to remove a radical from the denominator of a fraction through a process called rationalizing the denominator.

### 7. Addition and Subtraction Using Radical Notation

There are specific rules governing adding and subtracting radical expressions. This lesson will describe these rules and give examples of how they are used.

### 8. Multiplying Radical Expressions with Two or More Terms

Multiplying radical expressions with more than two terms can be confusing. This lesson will take some of the confusion away by giving clear steps for multiplying these expressions. It will also provide some examples to help solidify the steps.

### 9. Solving Radical Equations: Steps and Examples

Solving radical equations is not any more difficult than solving other algebraic equations. This lesson will show you how to solve equations containing a square root and give some real-world examples.

### 10. Solving Radical Equations with Two Radical Terms

Solving equations with two radical terms takes some patience and care, but it really is not difficult. This lesson will show you the steps to solve these more complicated equations plus give you some examples to follow.

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### Other Chapters

Other chapters within the CAHSEE Math Exam: Tutoring Solution course

- CAHSEE - Number Theory & Basic Arithmetic: Tutoring Solution
- CAHSEE - Problems with Decimals and Fractions: Tutoring Solution
- CAHSEE - Problems with Percents: Tutoring Solution
- CAHSEE - Problems with Algebraic Expressions and Equations: Tutoring Solution
- CAHSEE - Algebraic Linear Equations & Inequalities: Tutoring Solution
- CAHSEE - Problems with Exponents: Tutoring Solution
- CAHSEE - Overview of Functions: Tutoring Solution
- CAHSEE - Rational Expressions: Tutoring Solution
- CAHSEE - Calculations with Ratios, Percent & Proportions: Tutoring Solution
- CAHSEE - Matrices and Absolute Value: Tutoring Solution
- CAHSEE - Quadratics & Polynomials: Tutoring Solution
- CAHSEE - Geometry: Graphing Basics: Tutoring Solution
- CAHSEE - Graphing on the Coordinate Plane: Tutoring Solution
- CAHSEE - Measurement in Math: Tutoring Solution
- CAHSEE - Properties of Shapes: Tutoring Solution
- CAHSEE - Triangles, the Pythagorean Theorem & Congruency: Tutoring Solution
- CAHSEE - Perimeter, Area & Volume in Geometry: Tutoring Solution
- CAHSEE - Statistics, Probability & Working with Data: Tutoring Solution
- CAHSEE - Mathematical Reasoning: Tutoring Solution
- CAHSEE - Logic: Tutoring Solution