Vedic Mathematics - Finding Square of a number made easy

Find Square Of a number with Simple and faster Vedic Ways:
Vedic mathematic contains a lot of formulae (Sutra) that not only allows us to do calculations without pen and paper, it also makes our brain to act faster. Now-a-days, to crack in a competitive exam, we must look into two factors, they are SPEED and ACCURACY. By learning Vedic mathematics, one can achieve these two important factors to crack in any competitive exam.

This document contains formulae for finding out square of a number accurately without pen and paper. The formulae are easy to understand and are demonstrated in easy manner with examples.

1. Find Square of a number ending with 5:

1.1 Example: Let’s find out square of 25. a. Break the number to two parts with 2 as first part and 5 as second part
b. Find multiplication of 2 and (2+1), i.e 2 x 3 = 6
c. Find square of 5, i.e. 25
d. Hence, our answer, 25² = 6 25=625
1.2 Lets take another example, i.e. 65 a. 65 = 6 5
b. 6 x (6+1) = 42
c. Square of 5 = 25
d. Hence, 65² = 42 25 = 4225

1.3 Let’s take a 3 digit number, i.e. 125
a. 125 = 12 5
b. 12 x (12 + 1) = 156
c. Square of 5 = 25
d. Hence, 125² = 156 25 = 15625
This way this rule can be used to calculate square of numbers ending with 5 without help of pen and paper.

2. Find Square of a number which is adjacent to a number that ends with 0 or 5:

We can easily find out square of a number that ends with 0 or 5, e.g. 10, 15, 20, 25, 30 etc.
Now we will see how to find out square of an adjacent number like 11, 9, 16, 14, 21, 19 etc
2.1 Example: Let’s find out square of 31.
a. We know square of 30, i.e. 30² = 900
b. Now, 31² = 30² + (30 + 31) = 900 + 61 = 961

2.2 Lets find out square of 46
a. 45² = 2025
b. 46² = 45² + (45 + 46) = 2025 + 91 = 2116

2.3 Lets find out square of 71
a. 70² =4900
b. 71² = 70² + (70 + 71) = 4900 + 141 = 5041
Now, let’s find out numbers which are 1 less to numbers ending with 5 or 0
2.4 Find square of 14
a. 15² = 225
b. 14² = 15² – (14 + 15) =225 – 29 = 196
2.5 Find square of 29
a. 30² = 900
b. 29² = 30² – (29 + 30) = 900 – 59 = 841

3. Find out Square of a number near 100:

Let’s find out square numbers which are close to 100 and are lesser than 100.
3.1 Find square of 97
a. 97 is 3 less than 100 (i.e. -3)
b. 97² = 97 -3 / 03² = 94 / 09 = 9409 (There should be two digits (09 instead of 9) after ‘/’)
3.2 Find square of 96
a. 96 is 4 less than 100 (i.e. -4)
b. 96² = 96 -4 / 04² = 92 / 16 = 9216
3.3 Find square of 87
a. 87 is 13 less than 100 (i.e. -13)
b. 87² = 87 -13 / 13² = 74 / 169 =7569 (There should be two digits(69 out of 169), hence 1 is carry forwarded from 169 and added to 4 of 74)

Let’s find out square of numbers which are close to 100 and are greater than 100.
3.4 Find square of 103
a. 103 is 3 greater than 100 (i.e. +3)
b. 103² = 103 +3 / 03² = 106/09 = 10609
3.5 Find square of 107
a. 107 is 7 greater than 100 (i.e. +7)
b. 107² = 107 +7 / 07² = 114 / 49 = 11449
3.6 Find square of 113
a. 113 is 13 greater than 100 (i.e. +13)
b. 113² = 113 +13 / 13² = 126 / 169 = 12769 (1 is carry forwarded from 169)

I hope this material was helpful to you. I will add some more materials on Addition, Multiplication, Subtraction and Division and other formulae related to Algebra once I compile them.