How to square a number ? | Squaring Tricks | 25 Base Method

It is not possible to remember all the squares orally. But with some prefixed bases it became easy to calculate such Squares

For Faster calculation speed, it is very essential to learn Multiplication Tables up to 30 (must), Squares up to 60 & Cubes up to 30.

In some critical conditions (such as during live examination) when the timer is continuously running and when you can't remember the basics these methods work.   

Here, in this article we will learn how to find a square of a number using 25 as base.

➤ Divide the result portion in two parts.

Firstly, we will compare the given number with 50.

if the given number is less than 50, (let's assume by 'n' units) we will simply subtract it from the base (i.e. 25)

We will write it in the first part. 

➤ We will Calculate Square of 'n' and write it in the second part. 

(Note that if the second part contains 3 digit number we will simply carry it and add it in the first part.)

So let's understand this method by some examples.

For Ex.  (56)²

Step 1 :- As 56 is greater than 50 by 6 (hence, here n= 6) we will add it to the base 25 which results 31. 

Step 2 :- Square of 6 which is 36.
Final Result :- 3136.

For Ex.  (43)²

Step 1 :- As 43 is smaller than 50 by 7 (hence, here n= 7) we will subtract it from the base 25 which results 18.

Step 2 :- Square of 7 which is 49.
Final Result :- 1849.

For Ex.  (63)²

Step 1 :- As 63 is greater than 50 by 13 (hence, here n= 13) we will add it to the base 25 which results 38 

Step 2 :- Square of 13 which is 169. (Here we got 3 digit number hence 1 will get carried and we will add it in 38)

Final Result :- 3969.

 For Ex.  (34)²

Step 1 :- As 34 is smaller than 50 by 16 (hence, here n= 16) we will subtract it from the base 25 which results 9

Step 2 :- Square of 14 which is 256 (Here we got 3 digit number hence 2 will be carried and we will add it in 11)
Final Result :- 1156.

Problems For Practice

1)  (37)²

2)  (53)² 

3)  (44)²

4)  (39)² 

5)  (62)² 

6)  (47)² 

7)  (58)² 

8)  (41)² 

9)  (64)² 

10)  (36)² 

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