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# Squares & Perfect Squares – Explanation & Examples

In mathematics, a square is a product of a whole number with itself. For instance, the product of a number 2 by itself is 4. In this case, 4 is termed as a perfect square.

A square of a number is denoted as *n* × *n. Similarly*, the exponential notation of the square of a number is *n *^{2}, usually pronounced as “*n*” squared. Square numbers are usually non-negative.

## What is a Perfect Square?

A perfect square is a number that is generated by multiplying two equal integers by each other. For example, the number 9 is a perfect square because it can be expressed as a product of two equal integers: 9 = 3 x 3.*The first 25 perfect squares can be generated as shown in the table below:*

*Example 1*

Integer | Perfect square |

1 x 1 | 1 |

2 x 2 | 4 |

3 x 3 | 9 |

4 x 4 | 16 |

5 x 5 | 25 |

6 x 6 | 36 |

7 x 7 | 49 |

8 x 8 | 64 |

9 x 9 | 81 |

10 x 10 | 100 |

11 x 11 | 121 |

12 x 12 | 144 |

13 x 13 | 169 |

14 x 14 | 196 |

15 x 15 | 225 |

16 x 16 | 256 |

17 x 17 | 289 |

18 x 18 | 324 |

19 x 19 | 361 |

20 x 20 | 400 |

21 x 21 | 441 |

22 x 22 | 484 |

23 x 23 | 529 |

24 x 24 | 576 |

25 x 25 | 625 |

## How can you tell if a number is a Perfect Square?

There are many ways of determining if a number is perfect. A given number can be checked whether it is a perfect square using repeated division by prime factors.

*Example 2*

For example, to check whether 441 is a perfect square:

- Start by factorizing a number.

441 = 3 × 3 × 7 × 7

- Both numbers exist twice. Make two sets.

441 = 3 × 7 × 3 × 7 - Multiply them.

= 21 × 21

- It can be written as

= 21^{2}

- Hence, 441 is a perfect square.

You can also check whether a given number is a perfect square by finding the number’s square root. If the square root of a number is a whole number, then the number is a perfect square

For instance, the square root of 16 is 4. The square root of a number like 24 is not a whole number. Therefore, 24 is not a perfect square.