Theory:

Square and Square numbers:
  
In our earlier classes, we learned about power and exponent. When the exponent of a natural number is \(2\), the number has to be multiplied by itself which is called as square, and the obtained number is called a square number or a perfect square.
  
Square:
When the exponent of a natural number is \(2\), the number has to be multiplied by itself, and this is called square.
Sqaure3.PNG
 
For example: 32, 62, 112, 142.
 
Square number:
  
We know that the area of the square is a×a. That is multiplying the side by itself we get the area of the square.
 
Similar to this concept square of a number is obtained by multiplying it by itself.
 
That is if a×a=b. Therefore a2=b this is also true. Then we can say that the number \(b\) is the square of number \(a\).
 
For example:
 
32=3×3=962=6×6=36112=11×11=11142=14×14=196
 
Now the following table consists of squares of first \(20\) numbers. Students are advised to memorize it.
 
Number
Square
Number
Square number
1
12 \(= 1 × 1 = 1\)
11
112 \(= 11 × 11 = 121\)
2
22 \(= 2 × 2 = 4\)
12
122 \(= 12 × 12 = 144\)
3
32 \(= 3 × 3 = 9\) 
13
132 \(= 13 × 13 = 169\)
4
42 \(= 4 × 4 = 16\)
14
142 \(= 14 × 14 = 196\)
5
52 \(= 5 × 5 = 25\)
15
152 \(= 15 × 15 = 225\)
6
62 \(= 6 × 6 = 36\)
16
162 \(= 16 × 16 = 256\)
7
72 \(= 7 × 7 = 49\)
17
172 \(= 17 × 17 = 289\)
8
82 \(= 8 × 8 = 64\)
18
182 \(= 18 × 18 = 324\)
9
92 \(= 9 × 9 = 81\)
19
192 \(= 19 × 19 = 361\)
10
102 \(= 10 × 10 = 100\)
20
202 \(= 20 × 20 = 400\)