## Squares and Square Roots

Table of Contents

## How to Square A Number

To square a number:

**Multiply the number by itself.**

What is 4 squared?

4 squared = 4 × 4 = 16

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

**4**^{2}** = 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 0^{2} to 10^{2}

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) ?

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?**

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:

(−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”

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 4^{th} 2016 is a Square Root Day, because the date looks like 4/4/16

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