#### notes

Following table shows the squares of numbers from 1 to 20.

Number |
Square |
Number |
Square |

1 | 1 | 11 | 121 |

2 | 4 | 12 | 144 |

3 | 9 | 13 | 169 |

4 | 16 | 14 | 196 |

5 | 25 | 15 | 225 |

6 | 36 | 16 | 256 |

7 | 49 | 17 | 289 |

8 | 64 | 18 | 324 |

9 | 81 | 19 | 361 |

10 | 100 | 20 | 400 |

We observ that the square number ends with either 0 or 1 or 4 or 5 or 6 or 9 at its unit's place. We say that a square number always as will either 0 , 1 , 4 , 5,6 and 9T it's unit's place .

The following square numbers end with digit 1.

Square |
Number |

1 | 1 |

81 | 9 |

121 | 11 |

361 | 19 |

441 | 21 |

We say that if a number has 1 or 9 in the units place, then it’s square ends in 1.

Let us consider square numbers ending in 6.

Square |
Number |

16 | 4 |

36 | 6 |

196 | 14 |

256 | 16 |

when a square number ends in 6, the number whose square it is, will have either 4 or 6 in unit’s place.

Consider the following numbers and their squares.

We observe that a square number always has an even number of zeros at its end. A number with odd number of zeros is never a square of any number.