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Home >> Numbers >> Square Numbers >> Properties of Square Numbers >> Property 7 >>

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.




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