Math 20-1

Chapter 5 Radical Expressions and Equations

Lesson 5.3   Radical Equations

Support Documents

Answer pages

You should be checking your work for EVERY question you do!

To make that easy, you can download the solutions files which have the answers for all the practice problems in the text.

You can print it, though it would be a lot of pages.

I think the best choice would be to keep the files handy, and have them open and ready every time you are working on math.

This saves you the time of flipping to the back of the book every time you need to check an answer.

FOLDER LINK

Formula Page

Math 20-1 is an academic course and you will be expected to memorize a lot of what you are covering in class.

Your teacher will have expectations for the things you will see on a formula page.

The link below is to formula page that you can download and print to use with your course.

You may or may not be allowed to use this on tests, and you may or may not be allowed to ADD your own notes to these pages.

Use of this page depends on your teacher.

What goes on this page is also subjective, so it is subject to change!

Formula Page

Focus on...

Lesson Objectives

• 	solving equations involving square roots

• 	determining the roots of a radical equation algebraically

•	identifying restrictions on the values for the variable in a radical equation

• 	modelling and solving problems with radical equations

Focus on...  Activity

The FOCUS section introduces the main concept that will be covered in the lesson.

TEXT Page 294

Read through the  Focus  section at the top of page 294 in  your textbook.

Investigate  Radical Equations

The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 294 - 295

Read/Work through the  Investigate  section on Pages 294 - 295 in your textbook.

If you are working on your own,  answer the questions, AS BEST YOU CAN, before you view the Tutorial that follows.
Once you have done that,  view the video for help with this section.

Demonstration

Video Tutorial  INV A

I encourage you to DO the investigation as it’s given in the textbook!
However, in the interests of time, and to hopefully make it easier to DO this, you can accomplish all the goals of the investigation using the demonstration below.

Investigation

Question 3

Video Tutorial

Table Values.   The cell below has the table values, rounded to the nearest tenth.
Reveal the cell by clicking on the disclosure icon

Question 3  Table values

Question 4

Question 4
You could plot the points to see if they are on a line.
They aren’t....
The graph

Question 6

Video Tutorial Question 6   INV 3

Question 7

My computer simulation can be modified to work in 1 cm increments.
I would change this question and ask you to SOLVE for the value of h when v = 25
Video Tutorial  INV D

Question 8

I honestly must be missing something here.
The textbook gives an answer of 10 which my computer can verify.
But I can’t see an easy way to get that answer.
If you approximate...?  The answer is 10  (the difference in those values)

v[h_]:=100 - (Sqrt[(100^2)-(h^2)])

v[5(Sqrt[199])+5]- v[5(Sqrt[199])-5]//FullSimplify

Link the Ideas

Link the Ideas summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Page 295

Read/Work through the  Link the Ideas  section on Page 295 in your textbook.

Examples

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example 1  Solve an Equation With One Radical Term

TEXT Page 296

Work through Example 1 on Page 296 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 2  Radical Equation With an Extraneous Root

TEXT Page 297

Work through Example 2 on Page 297  in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 3  Solve an Equation With Two Radicals

TEXT Page 298

Work through Example 3 on Page 298 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

NOTE!   This question has a MESSY answer, so it’s NOT like the example.
I think it’s only fair in these kinds of questions to tell you whether to give approximate answers or not.
I will do the question with EXACT answers to illustrate....  but it’s super hard....

Video Tutorial

Example 4  Solve Problems Involving Radical Equations

TEXT Page 299

Work through Example 4 on Page 299 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Key Ideas

Key Ideas summarizes the main new concepts of the lesson.

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

Check Your Understanding    (Practice Problems)

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

NOTE!
There are MANY practice questions.
In the interests of time,  I will be selectively skipping some of them.
You have access to the solutions, and you can use those for help as needed.
If the presentation seems straight-forward, I won’t create a video.
I’m hoping that as this course continues to be developed, that if MORE HELP is needed for a specific question,  the missing videos can be added at a later date.

Types of Practice Problems

Practice 
These questions allow you to check your understanding of the concepts. 
You can often do the first few questions by checking the Link the Ideas notes or by following one of the worked Examples.

Apply 
These questions ask you to apply what you have learned to solve problems. 
You can choose your own methods of solving a variety of problem types.

Extend 
These questions may be more challenging. 
Many connect to other concepts or lessons. 
They also allow you to choose your own methods of solving a variety of problem types.

Create Connections
These questions focus your thinking on the Key Ideas and also encourage communication. 
Many of these questions also connect to other subject areas or other topics within mathematics.

Mini Lab
These questions provide hands-on activities that encourage you to further explore the concept you are learning.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

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