Answer:
The square root of 4489 is:
Explanation:
To find the square root by división method you must do the next:
1. you write the square root:
2. You separe the number inside the square root in groups of two digits, begining by the right (in this case doesn't matter, because we have 4 digits, but remember this when the number has an odd number of digits):
√44 89
3. You must find a whole number which squaring gives us a number equal to or less than our first pair of digits (44), in this case is 6, because 6*6 = 36 and, if we take 7, 7*7 = 49 (we would pass):
√44 89 ║6
4. Now, we subtract the squaring of the number obtained to our first pair of digits:
√44 89 ║6
-36
= 8
5. We duplicate the root obtained (6) and we lower the next pair of digits next to the result of the previous subtraction, but this time we make pairs of digits from the left:
√44 89 ║6
-36 ║12
= 88 9
6. We divide 88 (our pair of digits) in 12 (the double of the obtained root):
88 ÷ 12 = 7.3333333 (we approximate to 7)
7. We put the number obtained in the division (7) to the right side of the double of the obtained root (12) and we multiply by this too:
√44 89 ║6
-36 ║127 * 7 = 889
= 88 9
8. we subtract the number obtained in the multiplication to the digits we order in pairs (889):
√44 89 ║6
-36 ║127 * 7 = 889
= 88 9
- 889
= 0
9. We raise the number that we multiply by twice the previous root found, as another digit of the root:
√44 89 ║67
-36 ║127 * 7 = 889
= 88 9
- 889
= 0
As you can see, the square root of 4489 with this method gave us the result 67.