Square of Odd Number leads to Odd Square Number

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

Before you understand this property, you are advice to read: What are Square Numbers ? What are Odd Numbers ? Observe the following Table 1: 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 10 numbers. You can observe that numbers (highlighted in yellow) are odd and their corresponding square numbers (highlighted in green) are also odd. Let's try few more square numbers as shown in table 2 and table 3: Table : 2 Table : 3 Natural Number Square Number 41 1681 42 1764 43 1849 44 1936 45 2025 46 2116 47 2209 48 2304 49 2401 50 2500 Natural Number Square Number 71 5041 72 5184 73 5329 74 5476 75 5625 76 5776 77 5929 78 6084 79 6241 80 6400 In these tables also you will observe the same pattern which you observed in Table 1 i.e. numbers (highlighted in yellow) are odd and their corresponding square numbers (highlighted in green) are also odd. So this explain the property of square number that: Square of Odd numbers leads to Odd Square Number only.