Question

Evaluate 298116 by square root division method

Answer 1

I think you are being asked to evaluate the square root of 298116 by division method. Here is how its done:

             5 4 6
------------------------------------
     5 | 2 9 8 1 1 6
        | 2 5
        |------------ 
 104 | 0 4 8 1
        | 0 4 1 6
        |--------------
1086| 0 0 6 5 1 6
        | 0 0 6 5 1 6
        |------------------
        | X X X X X X
         ------------------
 
Please feel free to ask if something is not clear.

Here are the steps you will need to follow:

Step 1:
We find the largest square smaller than 29, that's 25. Subtract the 25 from the 29, which leaves 4, and enter a 5 as the first digit of your quotient.

Step 2:
Take the remainder 4 and 'bring down' the next pair of digits (81 as it happens) to make 481.
 
Step 3:
Use the first digit of our quotient 5 but double it (10) and make that ten times bigger (100). Now find 'something'- a single digit, so that one hundred and 'something' times that same 'something' is as large as possible but less than the 481.
 (i.e)104 times 4 makes 416, so 4 is the digit we want (105 times 5 would have been too big). So we add another digit to the quotient, which is 4. (so far we have 54 in the quotient)

Step 4:
Subtract the 416 from the 481. We are left with 65 as the remainder. Next 'bring down' the next pair of digits (so we are now aiming for 6516).

The digits we have so far in the quotient are 5 and 4. Double 54 and then make it ten times bigger (1080). Use the same technique as before: find one thousand and eighty 'something', times 'something', that gets as close as possible to 6516 without exceeding it.

Our third digit will be 6, 1086 times 6 is 6516 (as 1084 times 4 would be too large).

Step 5:
Subtract 6516 from 6516 and we are left with no remainder.
       
Hence our final quotient is 546