Square Roots

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

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

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 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 at your GED Math test.

1. Find the square root(s) of \(121\).
A.
B.

Question 1 of 2

2. Find the square root(s) of \(100\).
A.
B.
C.

Question 2 of 2


 

Next Lesson: Exponents

 

Last Updated on January 5, 2021.

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