Vedic Mathematics - Squaring a Number More than the Base
In this article, we learn a simple technique of squaring a number more than its base. What does this mean? Read this article further and you would have the answers soon.
In order to square a number, a base is needed. All those numbers can be taken as a base that have a 1 and the rest number of zeroes with them (i.e. the complete round numbers like 100, 1000, 10000 etc.). The square of a number will have two parts, the left part and the right part. There is no limit for the left side, but the right side must have as many digits as the number of zeroes in the base i.e. if 100 is taken as base there should be 2 zeroes on the right side and if 1000 is taken as base then the number of digits on RHS should be 3.
If the number to be squared is greater than the base, then the difference between the number and the base is to be added in the number instead of subtracting. Take a number 107. Its base will be 100. The difference is 7. The right side will have square of difference i.e. (7)2 = 49. And the left side will be 107 + 7 = 114 (that is the sum of the number and the difference between the base and the number) So the square is 11449.
Let's take one more example, say you need to square the number 103. The number is 3 more than the base and square of 3 is 9 i.e. it has a single digit. Now on the right hand side you will write 09 and the left hand side will be 103 + 3 = 106. Thus the square of the number is 10609.
In case the square of the difference is a 3-digit number, then the third digit would be carried and added to the left hand side. Consider one number say 118. The difference is 18 ? (18)2 ? 324. Out of this 3-digit number, the third digit 3 would be taken to the left side. The left side would become 118 + 18 + 3 (Carried) = 139 and the square would be 13924.
Similarly for the higher numbers, you can take the larger bases like 1000, 10000, 100000 etc and the squares of the numbers can be found out using a similar technique.
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