# Ch 7: High School Algebra - Radical Expressions: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other high school algebra I work.
- Identify the radical expressions 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 high school algebra I tutoring solution will benefit any student who is trying to learn radical expressions and earn better grades. This resource can help students including those who:

- Struggle with understanding how to find the square root of a number, simplify expressions with square roots, identify radicands, factor radical expressions, rationalize denominators or any other radical expressions topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their radical expressions unit
- Cope with ADD or ADHD
- Want to get ahead in high school algebra I
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning radical expressions 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 high school algebra I tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn radical expressions 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 find the square root of a number.
- Be able to estimate square roots.
- Simplify square roots that are not a perfect square.
- Understand how to simplify expressions that contain square roots.
- Identify the radicands of radical expressions.
- Simplify radical expressions with perfect-square radicands.
- Factor radical expressions.
- Be able to simplify radical expressions that have radicands as powers.
- Multiply and simplify radical expressions.
- Divide radical expressions.
- Learn how 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.
- List the steps for solving radical equations.
- Solve radical equations with two radical terms.

### 1. How to Find the Square Root of a Number

What is a square root? In this lesson, we'll learn what a square root is and how to find it. We'll review a variety of examples in order to master the concept.

### 2. 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.

### 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. Radicands and Radical Expressions

It's easy to see that funky radical symbol and panic just a little bit. There are so many rules that go along with it, it's hard to keep up with them all. This lesson will help by describing what you should do when you are faced with a square root.

### 6. 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.

### 7. Factoring Radical Expressions

Watch this video lesson to learn how to apply the product rule to your radical expressions. Learn how this product rule actually helps you to simplify your radicals as well.

### 8. Simplifying Square Roots of Powers in Radical Expressions

Simplifying radical expressions that contain powers can be tricky. There are a few simple rules that will help you perform these simplifications with ease. This lesson will teach you how.

### 9. Multiplying then Simplifying Radical Expressions

Multiplying 2 or more radical expressions uses the same principles as multiplying polynomials, with a few extra rules for dealing with the radicals. This lesson will teach you how to multiply and then simplify radical expressions.

### 10. Dividing Radical Expressions

When dividing radical expressions, we use the quotient rule. This lesson will describe the quotient rule and how to use it to solve these radical expressions.

### 11. 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.

### 12. 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.

### 13. 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.

### 14. 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.

### 15. 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.

### 16. 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 High School Algebra I: Tutoring Solution course

- High School Algebra - Basic Arithmetic: Tutoring Solution
- High School Algebra - Solving Math Word Problems: Tutoring Solution
- High School Algebra - Decimals and Fractions: Tutoring Solution
- High School Algebra - Percent Notation: Tutoring Solution
- High School Algebra - Real Numbers: Tutoring Solution
- High School Algebra - Exponents and Exponential Expressions: Tutoring Solution
- High School Algebra - Algebraic Expressions and Equations: Tutoring Solution
- High School Algebra - Properties of Functions: Tutoring Solution
- High School Algebra - Matrices and Absolute Value: Tutoring Solution
- High School Algebra - Working With Inequalities: Tutoring Solution
- High School Algebra - Properties of Exponents: Tutoring Solution
- High School Algebra - Complex and Imaginary Numbers: Tutoring Solution
- High School Algebra - Algebraic Distribution: Tutoring Solution
- High School Algebra - Linear Equations: Tutoring Solution
- High School Algebra - Factoring: Tutoring Solution
- High School Algebra - Graphing and Factoring Quadratic Equations: Tutoring Solution
- High School Algebra - Properties of Polynomial Functions: Tutoring Solution
- High School Algebra - Rational Expressions: Tutoring Solution
- High School Algebra - Cubic Equations: Tutoring Solution
- High School Algebra - Quadratic Equations: Tutoring Solution
- High School Algebra - Measurement and Geometry: Tutoring Solution
- High School Algebra - Calculations, Ratios, Percent & Proportions: Tutoring Solution
- High School Algebra - Data, Statistics, and Probability: Tutoring Solution
- High School Algebra - Well-Known Equations: Tutoring Solution