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: x^{2} = x times x, or x・x This is the “Square of a Number” or the number squared.

The number x^{2} is called the square of the number x.

So, for example:

9^{2 }= 9・9 which equals 81. So, the number 81 is the square of our number 9.

4^{2} = 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 9^{2 }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 4^{2 }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 a^{2} = 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 a^{2} = 49. Now, two (2) numbers come to mind:

7^{2 }equals 49. So the number 7 is a square root of our number 49.

-7^{2 }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.

Next Lesson: Exponents

Last Updated on January 5, 2021.