Vedic Mathematics - Squares

Mathematics can be fun for those who like it and nasty for those who hate it. In any case, a good knowledge in mathematics is always an added advantage.
Vedic Mathematics provides methods for making calculations easier. It provides techniques for mental calculations. I have already described the techniques for Easy Multiplication in an earlier post.
To read it, please click the following link : Easy Multiplication
Here, an easy method to find the square of any two digit number mentally is described.




Numbers Beginning with 1

• Here the base number is 10.

Consider the example 14 * 14.

• First find the difference of the number from base number 10. (14 - 10 = 4)
• Add it with the number. This forms the first part of result. (14 + 4 = 18)
• Now find the square of last digit. It forms last part of the result. (4 * 4 = 16)
• If the last part contains more than one digit, add all digits except last to the first part. (18 / 16 --> 196)
• 14 * 14 = 196

Consider another example 17 * 17

•  17 - 10 = 7
• 17 + 7 = 24
• 7 * 7 = 49
• 24 / 49 --> 289
• 17 * 17 = 289

These steps are written for illustration only. You can calculate the results directly.
13 * 13 = 16/9 = 169
11 * 11 = 12/1 = 121
This method can be used for numbers from 11 to 19.


Numbers Beginning with 2

• The method is almost similar to the previous one.
• Here base number is 20. (20 = 10 * 2)

Consider the example 21 * 21

• Find the difference from the base number. (21 - 20 = 1)
• Add it with the number and multiply by 2. (1+ 21 = 22 * 2 = 44)
• This forms first part of result.
• Now find square of last digit. This forms second part. (1 * 1 = 1)
• 44 / 1 --> 441

Here, in the second step , the number is multiplied by 2. This is the only difference from the first method.

22 * 22 = 2*(22+2) / 4 = 484
26 * 26 = 64 / 36 = 676

Similarly this method can be extended for numbers beginning with 3, 4, .. , 9.

Using this technique, you can easily find the square of any two digit number mentally. Practise with more examples and do recommend this method to your friends.