Final answer:
The square root of 729 through division method is 27, obtained by using long division where each pair of digits from the number is divided starting from the largest place value.
Step-by-step explanation:
The question asks about finding the square root of 729 using the division method. To calculate this, we'll use long division. Place 729 inside the division symbol. Start by pairing the digits from right to left (in this case, 7, 2, and 9 are single digits without pairs). We'll look for a number which, when multiplied to itself, gives a product less than or equal to 72. This number would be 8. S
o, we place 8 above the division bar, and 8 below 72, and subtract to get a remainder of 8. Bring down 29 to the remainder, making it 829. Now, double the number above the division bar (which is 8) to get 16. We need to find a digit 'X' such that 16X×X gives a product less than or equal to 829. The number X is obviously 7. Thus, the division method reveals that the square root of 729 is 27 (since 8×627 equals 729 exactly).