Square Roots

Last Updated on February 14, 2024.

Square roots are numbers that, when multiplied by themselves, will give the original nonnegative numbers.

Example: 6 times 6 = 36 and −6 times −6 = 36.

This lesson is provided by Onsego GED Prep.

Video Transcription

Recall this: x² = x times x, or x・x This is the “Square of a Number” or the number squared.

The number x² is called the square of the number x.

So, for example:

9² = 9・9, which equals 81. So, the number 81 is the square of our number 9.
4² = 4・4, which equals 16. So, the number 16 is the square of our number 4.

Just above the video, we’ve put a “List of Squares” of all whole numbers from 0 (zero) through 25. Please check that out.

Square Roots
By the time you’ve mastered the concept of squaring whole numbers, you are all set for the inverse process of squaring: determining the square roots of whole numbers.

Above, we’ve seen that 9² equals 81.
We name that number 81 the square of our number 9.

We name that number 9, conversely, the square root of our number 81.

We’ve also seen that 4² equals 16. We name the number 16 the square of our number 4.
We name 4, conversely, the square root of our number 16.

Square Roots

So when a² = b, we call the number “a” a square root of the number “b.”
For example, let’s find the square roots of 49.

Well, to find a square root of the number 49, we need to think of a number in a way that a² = 49. Now, two (2) numbers come to mind:

7² equals 49. So the number 7 is a square root of our number 49.
-7² equals 49. So the number -7 is also a square root of our number 49.

So you notice that our number 49 has two (2) square roots, a positive one and a negative one.

List of Squares and Square Roots

A square is a number multiplied by itself.

0²= 0
1²= 1
2²= 4
3²= 9
4²= 16
5²= 25
6²= 36
7²= 49
8²= 64
9²= 81
10²= 100

Square Roots

The opposite operation of squaring a number is finding its square root, and square roots are written with the radical symbol “√0” over them.

The following is a list of common perfect square roots:

√0 = 0
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10

It may be a good idea if you would memorize this list.
This may well help you manage your time on your GED Math test.