Find the square root of 729 by the division method.

Consider the following steps to find the square root of 729.

Step 1: Place a bar over every pair of digits starting from the digit at one’s place. If the number of digits in it is odd, then the left-most single digit too will have a bar. Thus we have $\left(\overline{7} \overline{29}\right)$.

Step 2: Find the largest number whose square is less than or equal to the number under the leftmost bar (2² < 7 < 3²). Take this number as the divisor and the number under the leftmost bar as the dividend. Divide and get the remainder i.e., 3 (As per Fig:1).

Step 3: Bring down the number under the next bar (i.e., 29) to the right of the remainder. The new dividend is 329 (As per Fig:1).

Step 4: Double the quotient and enter it with a blank on its right (As per Fig:1).

Step 5: Guess the largest possible digit to fill the blank which also becomes the new digit in the quotient such that when the new digit is multiplied by the new quotient the product is less than or equal to the dividend. 

In this case, we see that 47 × 7 = 329. So, the new digit in the quotient is 7. Get the remainder (As per Fig:1).

Step 6: Since the remainder is 0 and no bar left, therefore, $\sqrt{729}=27$.