Square of all Natural Numbers ends with either 0 or 1 or 4 or 5 or 6 or 9 at its one's place

Property 1	Property 2	Property 3	Property 4	Property 5
Property 6	Property 7	Property 8

Before you understand this property, you are adviced to read: What are Natural Numbers ? What are Square Numbers ? Observe the following table: Table 1 Natural Number Square Number 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 Above table - 1 represents square of first ten natural numbers. You must have observed that the square of these natural numbers have either 0 or 1 or 4 or 5 or 6 or 9 at its one's place And none of them have 2 or 3 or 7 or 8 at its one's place. Let's try few some squares of natural numbers as shown in the following two tables: Table : 2 Table : 3 Natural Number Square Number 20 400 21 441 22 484 23 529 24 576 25 625 26 676 27 729 28 784 29 841 30 900 Natural Number Square Number 70 4900 71 5041 72 5184 73 5329 74 5476 75 5625 76 5776 77 5929 78 6084 79 6241 80 6400 Table - 2 represents squares of numbers from 20 to 30 Table - 3 represents squares of numbers from 70 to 80 In these tables also you will observe the same pattern which you observed in Table 1 i.e. square of these natural numbers have either 0 or 1 or 4 or 5 or 6 or 9 at its one's place And none of them have 2 or 3 or 7 or 8 at its one's place. So, this explains this property of square numbers that: Square of all Natural Numbers ends with either 0 or 1 or 4 or 5 or 6 or 9 at its one's place. Also we get that: If a Natural Number has 0 or 1 or 4 or 5 or 6 or 9 at its one's place, then the Natural Number is not always a Perfect Square. e.g. 120, 134, 125, 1000, 79 are not square numbers