How to find Square of a number ? | Squaring Tricks | 100 Base Method

We have already learnt 25 Base Method which can easily calculate squares of two digit numbers quickly. Here we will study, how to find squares using 100 as base. 

Using 25 Base Method and a daily consistent practice of it we can orally calculate squares from 25 to 75.   

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

Here, in this article we will learn how to find a square of a number using 100 as base.

➤ Divide the result portion in two parts.

Firstly, we will compare the given number with 100.

if the given number is less than 100, (let's assume by 'n' units) we will simply subtract it from the given number.

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.  (106)²

Step 1 :- As 106 is greater than 100 by 6 (hence, here n= 6) we will add it to the given number (i.e. 106) which results 112. 

Step 2 :- Square of 6 which is 36.
Final Result :- 11236.

For Ex.  (92)²

Step 1 :- As 92 is smaller than 100 by 8 (hence, here n= 8) we will subtract it from the given number (i.e. 92) which results 84 .

Step 2 :- Square of 8 which is 64.
Final Result :- 8464.

For Ex.  (112)²

Step 1 :- As 112 is greater than 100 by 12 (hence, here n= 12) we will add it to the given number (i.e. 112) which results 124.

Step 2 :- Square of 12 which is 144. (Here we got 3 digit number hence 1 will get carried and we will add it in 124)

Final Result :- 12544.

 For Ex.  (86)²

Step 1 :- As 86 is smaller than 100 by 14 (hence, here n= 14) we will subtract it from the given number (i.e. 86) which results 72

Step 2 :- Square of 14 which is 196 (Here we got 3 digit number hence 2 will be carried and we will add it in 72)
Final Result :- 7496.

Problems For Practice

1)  (82)²

2)  (109)² 

3)  (113)²

4)  (91)² 

5)  (96)² 

6)  (103)² 

7)  (84)² 

8)  (88)² 

9)  (114)² 

10)  (119)² 

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