How to Find Square Root of Large Number

For large numbers, the above method will be very cumber some.

The square root of large numbers can be found by using an algorithm. It is explained through an example.

Example : Find the square root of 56,644

   ______
2 )56644 (2
  4

Enter the given number in a division bracket.
the digit is 5 and the nearest square less than 5 is 4
which is 2 * 2. enter one 2 as a divisor and one 2 as quotient.

         _______
40+3=43 ) 16644 ( 23
         129

Bring down the remainder.
Double the quotient in the previous step and multiply by 10. Enter that
in the divisor space. Add such a number so that the product of that number and the sum goes into the first few digits and perform the division.

Repeat the process till the remainder becomes zero.

           ______
460+8=468 ) 3744 ( 238
           3744 
             0

The final quotient is the square root of the given number.
So, the square root of 56,644 is + or - 238.
For the large numbers with decimal terms, decide the rounding place.

Follow the same algorithm till the quotient reaches to the place just lower to the rounding place and round up or round down as the case may be.

For example,

To find the square root of 22,987, rounded to the nearest thousandths, use the algorithm till the quotient reaches as 151.6146 and round the answer as 151.615.