Find square root of 7856809 using …

 1. Places a bar over every pair of digits from right to left (<—). Here, single digit 7 is left, so put a bar over 7.

    2. Take the digit 7. Find the greatest number whose square is 7 or less than 7. Such a number is 2. Write 2 at the top in the quotient and also 2 in the divisor. Subtract 22 i.e. 4 from 7. The remainder is 3.

    3. Bring down the pair of digits under the next bar (i.e. 85) to the right of the remainder. So new dividend is 385.

    4. Double the quotient (i.e. 2) to get 4 and enter it with a blank on its right at the place of new divisor.

    5. Find the largest possible digit to fill the blank which will also become the digit in the quotient, such that when the new divisor is multiplied by this digit in the quotient the product is less than or equal to the dividend. In this case 48 x 8 = 384, so we choose the new digit as 8. Place 384 under Subtract and get the remainder 1.

    6. Bring down the pair of digits under the new bar (i.e. 68) to the right of the remainder. So new dividend is 168.

    7. Double the quotient (i.e. 28) to get 56 and enter it with a blank on its right at the place of new divisor.

    8. Since no non-zero digit can fill the blank such that when the new divisor is multiplied by this new digit in the quotient so that the product is less than or equal to the dividend. Therefore, put 0 at blank in the divisor to get 560 and also put 0 in the quotient to get 280.

    9. Bring down the pair of digits under the next bar (i.e. 09) to the right of 168 to get 16809 as the new dividend. Now find the largest possible digit to be put at the right of the divisor 560 which will also become the new digit in the quotient, such that when the new divisor is multiplied by the new digit in the quotient the product is less than or equal to dividend.
In this case 5603 x 3 = 16809, so we choose new digit as 3. Place 16809 under the dividend 16809 and get remainder 0.

          = 2803