The document explains square numbers, defined as the product of a number multiplied by itself, with examples provided. It details properties of square numbers related to their unit digits, stating specific outcomes based on the last digit of the original number. Additionally, practice questions are included to test understanding of which numbers result in specific unit digits when squared.

1. Properties of Square
Numbers
By Parth Nagpal

2. What is a Square Number?
• A number when multiplied with itself gives a square number.
For Example,
2 × 2 = 4
3 × 3 = 9

3. Look at this table
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

4. Some Properties of Square Numbers
• The unit digit of a number ending in 0 is always 0.
• The unit digit of a number ending in 1 or 9 is always 1.
• The unit digit of a number ending in 2 or 8 is always 4.
• The unit digit of a number ending in 5 is always 5.
• The unit digit of a number ending in 4 or 6 is always 6.
• The unit digit of a number ending in 3 or 7 is always 9.
So, the unit digit of a square number is always 0,1,4,5,6,9.

5. Examples
Number Square
10 100
20 400
Number Square
9 81
11 121
Number Square
12 144
18 324
Number Square
14 196
16 256
Number Square
5 25
15 225
Number Square
13 169
17 289

6. Practice Questions
Q1. Square of which of the following numbers will have 1 in its unit place?
29, 25, 18, 31, 49, 52, 21, 55
Q2. Square of which of the following numbers will have 6 in its unit place?
24, 85, 13, 76, 54, 41, 58, 66
Q3. Square of which of the following numbers will have 9 in its unit place?
36, 23, 77, 84, 47, 53, 67, 22