Method to Calculate Squares of Numbers From 1 to 125, Without Using Pen or Calculator.

This is one the most interesting vedic mathematics techniques to learn. It is very easily to understand and remember. This will help you to do quick calculations which are otherwise lengthy.

You just need to remember squares of numbers from 1 to 25. The excel file is attached and you may print it for your quick reference.

Let's start learning !!

Step 1: Calculate Squares of Numbers From 26 to 75

Use following method for calculating squares of numbers from 26 to 75 :

a) Select a number ‘x’ ranging from 26 and 75.

Example: x = 38

b) Find difference of this number from 50 i.e. y = +|x – 50|. This difference would lie between -25 and 25.

Example: y = (38 – 50) = -12

c) Find square of this difference. y2 = (x – 50)2. Last two digits of this square would form the first and second place digits from right in the final square. Any third digit of this square would be carried forward to the digit at hundreds place.

Example: y2 = (-12)2 = 144

In the example, 44 would form the last two digits of the final square while 1 would be carried over to third digit from right.

d) Add the difference to 25 i.e. z = 25 + y. The resultant would form the third and fourth digit from the right

Example: z = 25 – 12 = 13

e) Bring together the first two and last two digits of the final square i.e. _z_ _y2_

Example: 13+144 = 1444

Step 2: Calculate Squares of Numbers From 76 to 125

Use following method for calculating squares of numbers from 76 to 125 :

a) Select a number ‘x’ ranging from 76 and 105.

Example: x = 121

b) Find difference of this number from 100 i.e. y = +|x – 100|. This difference would lie between -25 and 25.

Example: y = (121 – 100) = 21

c) Find square of this difference. y2 = (x – 100)2. Last two digits of this square would form the first and second place digits from right in the final square. Any third digit of this square would be carried forward to the hundreth place.

Example: y2 = (21)2 = 441

In the example, 41 would form the last two digits of the final square while 4 would be carried over to third digit from right.

d) Add the difference to the number itself i.e. z = x + y. This can also be written as z = (100 + 2y)

Ones and tens place digit of this number will form the third and fourth digit from right of the final square. Any third digit of this number would be carried forward to fifth place.

Example: z = 121 + 21 = 142 or z = 100 + (2*21) = 142

Here, 42 will form the thousands and hundreds digits of the final square. 1 will be carried forward as fifth digit

e) Bring together the first two and last two digits of the final square i.e. _z_ _y2_

Example: 142+441 = 14641