Squares and Square Roots

How to Square A Number

To square a number:

Multiply the number by itself.

Examples

What is 4 squared?

4 squared = 4 × 4 = 16

“Squared” is often written as a little 2 like this:

42 = 16

This says “4 Squared equals 16

(the little 2 says the number appears twice in multiplying)

Perfect Squares

The Perfect Squares (also called “Square Numbers“) are the squares of the integers:

Perfect Squares From 02 to 102

NumberSquare
00
11
24
39
416
525
636
749
864
981
10100

Negative Numbers

We can also square negative numbers.

What happens when we square (−7) ?

Answer:

(−7) × (−7) = 49

(because a negative times a negative gives a positive)

When we square a negative number we get a positive result.

Square Roots

A square root goes the other way:

What can we multiply by itself to get this?

Examples

Find a square root of 25

What can we multiply by itself to get 25?

A square root of 25 is 5, because when 5 is multiplied by itself we get 25.

So,

a square root of a number is a value that can be multiplied by itself to give the original number.

Negatives Roots

We discovered earlier that we can square negative numbers:

Examples

(−6) squared

(−6) × (−6) = 36

And of course 6 × 6 = 36 too.

So the square root of 36 could be −6 or +6

Perfect Square Roots

The Perfect roots are the roots of the integers:

SquareSquare Root
11 or -1
42 or -2
93 or -3
164 or -4
255 or -5
366 or -6
497 or -7
648 or -8
819 or -9
10010 or -10

The Square Root Symbol

This is the special symbol that means “square root“.

Use it like this:

√49 is 7

we say “square root of 49 equals 7”

Examples

What is √81 ?

81 = 9 × 9

in other words when we multiply 9 by itself (9 × 9) we get 81

So the answer is:

√81 = 9

Square Root Day

The April 4th 2016 is a Square Root Day, because the date looks like 4/4/16

The next after that is the May 5th 2025 (5/5/25)

Learn More

Simplifying Square Roots

Cube Numbers and Cube Roots

Negative Exponents

Fractional Exponents

Algebra Index

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