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Home >> Numbers >> Square Numbers >> Properties of Square Numbers >> Property 1 >>

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

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