Find the square root of 4096 using division method?

If you want to find out square root of any number by division method, you must follow these steps:

1. First of all, write the number of which you want to find out square root.
2. Make pairs from right side of the number. In case of 4096 there will be two pairs: 40 and 96.
3. Now you will have to find out the number whose square is less than or equal to 40 (as it is our first pair).

1 x 1 =1
2 x 2=4
3 x 3=9
4 x 4=16
5 x 5=25
6 x 6 =36
7 x 7=49

We can see here that square of 7 will be more than the 40. Hence we can use square of 6 I.e. 36.

Now write 36 below the 40 and 6 on the top ( quotient)
Now we will get a remainder of 4.
In this step write next pair i.e. 96 along with the remainder 4 ( now the number will be 496)
Now we will have to multiply the 6 (quotuent) by 2 and write 12_ at left hand side of 496.
Find out the number whose square us less than or equal to the number 496.
121 x 1=121
122 x 2= 244
123 x 3=369
124 x 4=496
(In this step, you will have to add a digit with 12 and multiply by the same number and find out the number which is equal to or less than the 496).

As we can see that after using 4 we will get 496. So that the rremainder will be zero. And we will write 4 at the top along with the 6 and the answer will be 64.

Similarly, you can find out square root if any number by division method. Remember for 3 there will be only one pair from right and we will have to find out square of a number which is winter equal to or less than the single digit first.

In case of five digit number there will be two pairs from right and a single digit whose square is to be find out square of a number which is winter equal to or less than the single digit first.

The square root of 4096, by division menthid.
In this method, we have to take two numbers as one unit from our right-hand side 40 will be one unit and 96 will be the second unit. first, we have to consider 40. What is the maximum number which is less than 40 we get by multiplying one number with the same number 5x5 =25, 6X^=36, 7X7=49, 49 is greater than 40. So we will use six Now we will deduct 36 from the first two numbers that are 40. The remainder is 4 in 100s place and the number 496. We have to double the first number which we used for dividing that is 6 and the number will become 12. After 12 if we put 4 and multiply 124 with 4 it will be 496 without any remainder. Now we used 6 first and then 4. So the square root of 4096 is 64.

In our school times, we did not have any calculator or computer so we used the division method for finding out the square root of a number and even if it did not have an exact square root we found the value to some decimal places also. Let me describe the method in detail.

Whichever number we want to find the square root, starting from right most digit (unit place) we should make pairs of two numbers and if one number remains then it will be treated like a singleton pair. Generally we put a bar on the pairs to distinguish them from each other. For example if we want to find out the square root of 81729 then we would place the bar like this -
_ ___ ___
8 17 29

Now we will find a number as divisor which when multiplied by itself gives the dividend 8 or less than 8 but never more than 8. Such a number is 2 so we divide 8 by 2 in this fashion and get the first quotient as 2 and remainder as 4. Now bring down the next pair and place it on the right side of 4 making it 417. Now 417 becomes the new dividend. Next step is double the quotient and now add one number to its right side in such a way that the multiplication of this resulting number with the number itself is less than or equal to 417. That number in this case will be 8 and so the second quotient is 8 and remainder is 417 - (48 x 8) = 133. Now bring down the next pair that is 29 and keep it in right side of 133 making the figure as 13329 and again double the quotient obtained so far and repeat the process.

We have to continue like that and when the pair 29 is exhausted then if the remainder is not zero then the square root can be found up to certain decimal places and for that we have to add a pair of 00 as many times as to which we want to find the square root precisely. Method is same that every time the quotient is to be doubled and a next quotient is found which satisfies the condition of equal to or less than the dividend and remainder is obtained. The sequence of quotient is the answer to the problem and is the square root of the number.

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.

In this method we have to make the pairing of the digit from right side. Like in 4096 we will have two pairs 40 and 96.

Now for the digit 40 will divide it by square root 6X6=36

Remainder is 4 and the next digit will be 496 and next digit with which we have to divide will 6+6=12

121X1=121
122X2=244
123X3= 369
124X4=496

So the quotient is 64 and the square root is 64X64=496.