In the exponents unit we took a close look at exponents and powers. You may want to review the lesson on exponents before starting this lesson.
Let's get started.
Another term for raising a number to the 2nd power is "squaring a number". For example:
22 = 4. This can be read as 2 "squared" equals 4. This means that 2 x 2 = 4.
32 = 9. This can be read as 3 "squared" equals 9. This means that 3 x 3 = 9.
42 = 16. This can be read as 4 "squared" equals 16. This means that 4 x 4 = 16.
As you've probably discovered in Math, there is always an "opposite" operation. So, can you guess the opposite operation for "squaring" a number?
You've got it - taking the "square root" is the opposite of squaring a number!
Let's take a look at the symbols.
Before we dig in, let's look at some familiar vocabulary. The symbol used for identifying roots is called the radical sign.
The number inside the radical sign is called the radicand.
When you start Algebra 2, you will also learn that if you are working with cube roots, or fourth roots..., there will be another number called the index. We'll worry about the index later.
Take a look at the diagram below to further explain these definitions.
Take a look at the chart below for a list of the most common square roots.
It is a common mistake to identify the square root of 4 as 2 and -2.
Wow! We've covered a lot in this lesson, but let's look at one more example.
When you take the square root of a fraction, simply take the square root of the numerator and the square root of the denominator. The answer remains a fraction. Take a look at the following examples.
Wow! We've accomplished a lot, and there's a lot more to learn. But, we'll take it one step at a time, and soon you'll have a solid understanding of quadratics.
Now, you are ready to start our first lesson on solving quadratic equations.
Quadratic Equations Unit
Sign Up for Algebra Class E-courses
"I'd like to start off by relaying my sincerest gratitude for your dedication in teaching algebra. Your methodology is by far the simplest to follow, primarily because you take the time to include the small steps in between that most other teachers leave out.
It helps to know why you are doing something. I am 45 and heading to college to get my BS in Business. I need to brush up, hence the visit to your site. Great Job!"
Jimmy - United States
"I stumbled onto your site after I found out that I needed to use some fundamental algebra for an assignment. Turns out I had forgotten some things and your great site helped me remember them like "that" (snap of fingers). The organization of the site let me find exactly what I was looking for so easily. Kudos to you for maintaining such a great resource for students of all ages!"
Tom - United States
"I just wanted to write and basically thank you for making such a wonderful website! I'm 20 years old and about to take a basic placement test for college. I wanted to brush up on my Algebra skills and I stumbled upon your site. I'm amazed at how simple you make it and how fast I'm remembering Algebra! I don't remember getting most of the answers right when I had an actual teacher in front of me teaching this. Thanks a lot!"
Elizabeth - United States
"I am a pensioner living in South Africa. I stumbled on your website, the best thing that could ever happen to me! Your course in Algebra has helped me a lot to better understand the different concepts. Thank you very much for sharing your skills for teaching math to even people like me. Please do not stop, as I am sure that your teachings have helped thousands of people like me all over the world."
Noel - South Africa
This is an amazing program. In one weekend I used it to teach my Grade 9 daughter most of the introductory topics in Linear Relations. I took her up to Rate of Change and now she can do her homework by herself.
Reg - United States
Copyright © 2009-2014 Karin Hutchinson ALL RIGHTS RESERVED