What are square numbers ?

When a number is multiplied by itself, the product is called as a ‘Square Number’.

Why Square Numbers:

As squares have all the sides equal, in a similar manner a square number is the product of two number which are equal (i.e. the number itself).

Area of a square = Side \(\times\) Side

Square number = a \(\times\; a \; = a^{2}\)

Side of square (in cm) |
Area of square (in cm^{2}) |

3 |
3 × 3 = \(3^{2}\) = 9 |

5 |
5 × 5 = \(5^{2}\) = 25 |

7 |
7 × 7 = \(7^{2}\) = 49 |

8 |
8 × 8 = \(8^{2}\) = 64 |

Numbers such as 1, 4, 9, 16, 25, 36, 49, 64, etc. are special numbers as these are the product of a number by itself.

If we express a number (x) in terms of square of any natural number such as a^{2}, then x is a square number. For example 100 can be expressed as 10 × 10 = 10^{2}, where 10 is a natural number, therefore 100 is a square number. Whereas, the number 45 cannot be called as a square number because it is the product of numbers 9 and 5. The number is not multiplied by itself. **Square numbers** can also be called as perfect square numbers.

**List of squares for numbers less than 60 ^{2} = 3600**

0^{2} = 0 |
10^{2} = 100 |
20^{2} = 400 |
30^{2} = 900 |
40^{2} = 1600 |
50^{2} = 2500 |

1^{2} = 1 |
11^{2} = 121 |
21^{2} = 441 |
31^{2} = 961 |
41^{2} = 1681 |
51^{2} = 2601 |

2^{2} = 4 |
12^{2} = 144 |
22^{2} = 484 |
32^{2} = 1024 |
42^{2} = 1764 |
52^{2} = 2704 |

3^{2} = 9 |
13^{2} = 169 |
23^{2} = 529 |
33^{2} = 1089 |
43^{2} = 1849 |
53^{2} = 2809 |

4^{2} = 16 |
14^{2} = 196 |
24^{2} = 576 |
34^{2} = 1156 |
44^{2} = 1936 |
54^{2} = 2916 |

5^{2} = 25 |
15^{2} = 225 |
25^{2} = 625 |
35^{2} = 1225 |
45^{2} = 2025 |
55^{2} = 3025 |

6^{2} = 36 |
16^{2} = 256 |
26^{2} = 676 |
36^{2} = 1296 |
46^{2} = 2116 |
56^{2} = 3136 |

7^{2} = 49 |
17^{2} = 289 |
27^{2} = 729 |
37^{2} = 1369 |
47^{2} = 2209 |
57^{2} = 3249 |

8^{2} = 64 |
18^{2} = 324 |
28^{2} = 784 |
38^{2} = 1444 |
48^{2} = 2304 |
58^{2} = 3364 |

9^{2} = 81 |
19^{2} = 361 |
29^{2} = 841 |
39^{2} = 1521 |
49^{2} = 2401 |
59^{2} = 3481 |

## Odd and Even square numbers

- Squares of even numbers are even, i.e, (2n)
^{2}= 4n^{2}.

- Squares of
**odd numbers**are odd, i.e, (2n + 1) = 4(n^{2}+ n) + 1.

- Since every odd square is of the form 4n + 1, the odd numbers that are of the form 4n + 3 are not square numbers.

## Special Properties of square numbers

Here we have covered square numbers and their properties, you can refer completing the square method which by following the link provided. To learn more about other topics download BYJU’S – The Learning App and learn the subjects in an intereactive and innovative ways.