Find the square root of 4489 by division method.

To find the square root of 4489 by the long division method, you can follow these steps:

Group the digits of the number in pairs, starting from the decimal point (if there is one). In this case, 4489 is a whole number, so we don't have a decimal point to worry about. So, group the digits as follows:

44 | 89

Find the largest number whose square is less than or equal to the leftmost group (44 in this case). The largest square less than or equal to 44 is 6^2, which is 36. Write 6 as the first digit of the square root.

6 | 89

Subtract the square you found in step 2 from the leftmost group and bring down the next pair of digits to the right. Your calculation now looks like this:

6 | 89

36
Now, you need to find a digit to add after the 6 to make a new divisor that, when multiplied by the new divisor and the result added to the previous result, is as close to 89 as possible without exceeding it. You can try different digits, starting from 0.

Let's try 0:

60 | 89
- 36

Subtract 36 from 89, and you get 53. Bring down the next pair of digits (89 becomes 5389), and you're ready for the next step.

Now, you need to find a digit to add after the 0. You're looking for a digit such that when it's multiplied by the new divisor and the result is added to the previous result, it's as close to 5389 as possible without exceeding it. Again, try different digits.

Let's try 1:

601 | 5389
- 361

Subtract 361 from 5389, and you get 5028. Bring down the next pair of digits (89 becomes 502889), and continue.

Now, you need to find a digit to add after the 1. You're looking for a digit such that when it's multiplied by the new divisor and the result is added to the previous result, it's as close to 502889 as possible without exceeding it.

Let's try 8:

6018 | 502889
- 48144

Subtract 48144 from 502889, and you get 454745. Bring down the next pair of digits (89 becomes 45474589), and continue.

Now, you need to find a digit to add after the 8. You're looking for a digit such that when it's multiplied by the new divisor and the result is added to the previous result, it's as close to 45474589 as possible without exceeding it.

Let's try 9:

60189 | 45474589
- 54161161

Subtract 54161161 from 45474589, and you get a negative result, which means you have gone too far. So, you need to try a smaller digit.

Let's try 8:

60188 | 45474589
- 54150444

Subtract 54150444 from 45474589, and you get 464155.

Bring down the next pair of digits (89 becomes 46415589), and continue the process.

Now, you need to find a digit to add after the 88. You're looking for a digit such that when it's multiplied by the new divisor and the result is added to the previous result, it's as close to 46415589 as possible without exceeding it.

Let's try 5:

601885 | 46415589
- 54151825

Subtract 54151825 from 46415589, and you get 2253764.

Bring down the next pair of digits (89 becomes 225376489), and continue the process.

Now, you need to find a digit to add after the 885. You're looking for a digit such that when it's multiplied by the new divisor and the result is added to the previous result, it's as close to 225376489 as possible without exceeding it.

Let's try 2:

6018852 | 225376489
- 21675408

Subtract 21675408 from 225376489, and you get 868951.

Bring down the next pair of digits (89 becomes 86895189), and continue the process.

Now, you need to find a digit to add after the 8852. You're looking for a digit such that when it's multiplied by the new divisor and the result is added to the previous result, it's as close to 86895189 as possible without exceeding it.

Let's try 8:

60188528 | 86895189
- 60150784

Subtract 60150784 from 86895189, and you get 26744405.

Bring down the next pair of digits (89 becomes 2674440589), and continue the process.

Now, you need to find a digit to add after the 88528. You're looking for a digit such that when it's multiplied by the new divisor and the result is added to the previous result, it's as close to 2674440589 as possible without exceeding it.

Let's try 3:

601885283 | 2674440589
- 1805650569

Subtract 1805650569 from 2674440589, and you get 868790020.

Bring down the next pair of digits (89 becomes 86879002089), and continue the process.

Now, you need to find a digit to add after the 885283. You're looking for a digit such that when it's multiplied by the new divisor and the result is added to the previous result, it's as close to 86879002089 as possible without exceeding it.

Let's try 0:

6018852830 | 86879002089
- 60150748400

Subtract 60150748400 from 86879002089, and you get 26728253689.

Bring down the next pair of digits (89 becomes 2672825368989), and continue the process.

Now, you need to find a digit to add after the 8852830. You're looking for a digit such that when it's multiplied by the new divisor and the result is added to the previous result, it's as close to 2672825368989 as possible without exceeding it.

Let's try 3:

60188528303 | 2672825368989
- 1805650560909

Subtract 1805650560909 from 2672825368989, and you get 867174808080.

Bring down the next pair of digits (89 becomes 86717480808089), and continue the process.

Now, you need to find a digit to add after the 88528303. You're looking for a digit such