Ultimate Mathematics Tricks in Finding Squares of Numbers

 Easy math tricks. Aren’t they great? Little tricks and shortcuts to get you to your destination quicker and easier. And I have got another for you! This will enable you to calculate any two-digit perfect square. 

Did you know?

A square of any given number will always end in 0, 1, 4, 5, 6, or 9. This was evident in the table of squares that was published by mathematician Dr. Hutton, in the year 1781.

To find squares the method followed by most of you is by multiplying the number to itself.

A) How to Find the Square of Numbers Ending in 5 

Step 1:-

Separate 5 in the units place from the number and note down the square of 5 i.e. 25, and consider the number formed by the rest of the digits.

Step 2:-  

Multiply this number by  its successive number.

Step 3:-

Place the number 25 at the end of the product obtained. The new number thus formed is the square of the original number.

Example:-  Consider the number 45

45² =  4 x 5 | 5²  =  20 | 25 = 2025. 

B) How to Find the Square of Numbers Ending in 1

Step 1:-

Separate 1 in the units place from the number, and consider the number formed by the rest of the digits. 

Step 2:-

Obtain the square of this digit, and also its product with two.

Step 3:-

Place the digits of the squared value followed by the digit in the units place of the product. If there is more than one digit in the product, then other than the digit in the units place, add the rest of them to the squared value.

Step 4:-

Place the digit 1 at the end of the number obtained from the previous step. The number thus obtained is the square of the original number.

Example 1:- Consider the number 41 

41² =  4² | 4  x 2 | 1 = 16 | 8 | 1  =  1681.

Example 2:- Consider the number 61

61² =  6² | 6  x 2 | 1 = 36 | 12 | 1  =  (36+1) | 2 | 1 =  37 | 2 | 1 =  3721

C) How to Find Square of Numbers Ending other than 0, 1, 5 

Step 1:-   

Split the number present in units place and the number formed by rest of the digits by a vertical line in between them and draw a horizontal line below it.

Step 2:-

 Write the square of number present in units place to the left of vertical line below the horizontal line and square of number formed  by remaining digits to the right of vertical line below horizontal line. If the square of the number is one digit number then write it in the form of two digit number ( Example:- if the number is 3 then write the square of 3 as 09).

 Step 3:-

Multiply the separated numbers and split the product. Write the number present in the units place to the right of vertical line and the number formed by rest of the digits to the left of vertical line. Draw a horizontal line below it.

Step 4:-

Write the addition of respective numbers from step 2 and step 3 separated by a vertical line below the horizontal line.

Step 5:-                                          

Combine the numbers present to the left and right of vertical line.

Examples:-                 

5	4
25	16
+      4	0
29	16

Square of 54 is 2916

3	2
09	04
+      1	2
10	24

Square of 32 is 1024

6	6
36	36
+      7	2
43	56

Square of 66 is 4356

There are many more tricks of finding squares of two-digit number or three-digit number.

I am also going to share some more tricks in my next blog and also going to share links of some books of Vedic Maths which will help you in knowing many more other tricks and shortcut for fast calculation.

Stay tuned.

Links of sites for more examples:- 

Squares of number ending with 5:-

https://www.easymaths.in/2020/03/20/176/

Squares of number ending with 1:-

https://sites.google.com/site/qmtechniques/11-square-1---ending-number

Sources:- Google and Books of Vedic Maths 

                                                                                                - Khushal Jain