Theory:

We are well aware of doing the arithmetic operation like addition and subtraction, and we can use these operations to calculate the square of the number in a simple way.
 
In your earlier classes, you could have studied about the formula of (a+b)2, That is (a+b)2=a2+2ab+b2.
 
Similarly (ab)2=a22ab+b2
 
We can use the above two formulas to calculate the square of a number.
 
Let's see an example to understand this method clearly.
  
i) Calculate the square of 16.
 
We have to find the square of 16. That is 162
 
We can rewrite  162 as (15+1)2, (14+2)2, (13+3)2 and so on.
 
That is  (15+1)2 \(=\) (14+2)2 \(=\)  (13+3)2 \(=\) 162
 
To avoid complexity, we take (15+1)2 \(=\) 162.
 
Let \(a =\) 15 and \(b = 1\).
 
Now we substitute the values of \(a\) and \(b\) in (a+b)2.
 
(a+b)2=a2+2ab+b2(15+1)2=152+2(15×1)+12(15+1)2=225+2(15)+1(16)2=225+30+1256=256
 
Let's see another example using (ab)2=a22ab+b2 formula.
 
II) Calculate the square of 26.
 
We have to find the square of 26. That is 262
 
We can rewrite  262 as (271)2, (282)2, (293)2 and so on.
 
That is  (271)2 \(=\) (282)2 \(=\)  (293)2 \(=\) 262.
 
To avoid complexity, we take (271)2 \(=\) 262.
 
Let \(a =\) 27 and \(b = 1\).
 
(ab)2=a22ab+b2(271)2=2722(27×1)+12(151)2=7292(27)+1(26)2=72954+1676=676
 
Generally, we multiply the number by itself to find the square of the number, but if the number consists more than three digits like (\(888, 999, 1000, 1500\)), then we can prefer this method to find the square of the number easily.