Question

Find $\sqrt{729}$ using long division.

Answer 1

Steps involved in square root by long - division method
Step 1 : Place a bar over every pair of digits starting from the unit digit. If the number of digits in it is odd, then the left most single digit too will have a bar. Thus we have, 7 29. So 1st bar is on 29 and 2nd bar is on 7.

Step 2 : Find the largest number whose square is less than or equal to the 1st number, here it is '7'.
$(2^2<7<3^2)$. Here the we take 2. Divide and get the remainder (3 in this case).

Step 3 : Bring down the number under the next bar (i.e., 29 in this case) to the right of the remainder. So the new dividend is 329.

Step 4 : Add the divisor 2 and quotient 2 that gives us 4.
Step 5 : Think of a largest number in fill in the balnk in such a way that the product of a new divisor and this digits is equal to or less than 329 (new dividend). In this case $47\times 7=329$
As $47\times 7=329$ so we choose the new digit as 7. Get the remainder.

Step 6 : Since the remainder is 0 and no digits are left in the given number,
$\therefore \sqrt{729}=27$