While determining the square root of any number by means of division method, the numbers are calculated first. The numbers may be either odd or even. Now we have to move from left to right taking two numbers at a time. If the numbers are even, taking two numbers will not leave a lone pair but if the numbers are odd, one digit at the extreme right will indicate a lone pair.

This is applicable for all uneven numbers just as 3 digits, 5 digits, 7 digits and so on where we will get one digit at the extreme right. If the numbers are even digits, there will be no more lone a single digit.

Here the given number is 4096 for which square root is to found out.

On pairing we get two pairs 40 and 96. Now we would consider the number 40 lying in the location of right side. The square root 40 lies between the number 6 and 7 since the square of 6 is equal to 36 and the square of 7 is 49 which is greater than the number 40 and hence discarded. In no case the number should exceed 40.

Hence first number of the square root is 6.

Now writing 36 below 40 and on substracting 36 from 40, we get 4 and this 4 will be written as 496 taking the other left pair. In the extreme left side number 6 and again the same number is added and the resultant number is 12. We have to search the third number such that by putting a number accompanied 12, there will be complete division of 496. Here 4 is the third number making 124 and on multiplying with 4 we get 496.

Hence the square root of 4096 is 64.