# 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

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

## Negative Numbers

We can also square negative numbers.

What happens when we square (−7) ?

(−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:

 Square Square Root 1 1 or -1 4 2 or -2 9 3 or -3 16 4 or -4 25 5 or -5 36 6 or -6 49 7 or -7 64 8 or -8 81 9 or -9 100 10 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

√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)