Find the square root of the following numbers by division method.

• i. 1089
• ii. 2304
• iii. 7744
• iv. 6084
• v. 9025

To find the square roots of the given numbers using the division method, follow these steps for each number:

Square Root of 1089

1. Pair the digits from right to left: (10)(89).

2. Find the largest number whose square is less than or equal to 10. This is 3 (since 3² = 9).

3. Subtract 9 from 10 to get 1. Bring down the next pair (89) to make 189.

4. Double the divisor (3) to get 6. Now find a digit (x) such that (60 + x)x ≤ 189. The digit is 3 (since 63 * 3 = 189).

5. The square root of 1089 is 33.

Square Root of 2304

1. Pair the digits: (23)(04).

2. The largest number whose square is less than or equal to 23 is 4 (since 4² = 16).

3. Subtract 16 from 23 to get 7. Bring down 04 to make 704.

4. Double the divisor (4) to get 8. Find a digit (x) such that (80 + x)x ≤ 704. The digit is 8 (since 88 * 8 = 704).

5. The square root of 2304 is 48.

Square Root of 7744

1. Pair the digits: (77)(44).

2. The largest number whose square is less than or equal to 77 is 8 (since 8² = 64).

3. Subtract 64 from 77 to get 13. Bring down 44 to make 1344.

4. Double the divisor (8) to get 16. Find a digit (x) such that (160 + x)x ≤ 1344. The digit is 4 (since 164 * 4 = 656).

5. The square root of 7744 is 88.

Square Root of 6084

1. Pair the digits: (60)(84).

2. The largest number whose square is less than or equal to 60 is 7 (since 7² = 49).

3. Subtract 49 from 60 to get 11. Bring down 84 to make 1184.

4. Double the divisor (7) to get 14. Find a digit (x) such that (140 + x)x ≤ 1184. The digit is 8 (since 148 * 8 = 1184).

5. The square root of 6084 is 78.

Square Root of 9025

1. Pair the digits: (90)(25).

2. The largest number whose square is less than or equal to 90 is 9 (since 9² = 81).

3. Subtract 81 from 90 to get 9. Bring down 25 to make 925.

4. Double the divisor (9) to get 18. Find a digit (x) such that (180 + x)x ≤ 925. The digit is 5 (since 185 * 5 = 925).

5. The square root of 9025 is 95.

In summary, the square roots are:

• √1089 = 33
• √2304 = 48
• √7744 = 88
• √6084 = 78
• √9025 = 95