Find the square root of 1369 by long division method. Please, it’s a request to all to answer as soon as possible. Waiting for answers from all users and my special (one) user…
The Correct Answer and Explanation is:
✅ Correct Answer:
The square root of 1369 is 37.
🔢 Long Division Method Step-by-Step:
- Group the digits of 1369 from right to left in pairs:
→ 13 | 69 - Find the largest number whose square is less than or equal to 13:
→ 3² = 9 (ok),
→ 4² = 16 (too much),
So, use 3. - Place 3 in the quotient and also write 3 above 13:
- Subtract: 13 – 9 = 4
- Bring down next pair 69, so the new dividend is 469
- Double the quotient (3 × 2 = 6) and write it as the new divisor’s starting digit:
→ Think of a number X such that (60 + X) × X ≤ 469 Try:- X = 7: (60 + 7) × 7 = 67 × 7 = 469 ✅
So X = 7 works.
- X = 7: (60 + 7) × 7 = 67 × 7 = 469 ✅
- Put 7 in quotient next to 3 → Quotient = 37
- Subtract: 469 – 469 = 0
- Nothing more to bring down, division complete.
🧠 Explanation
Finding a square root through the long division method offers a systematic approach, especially for perfect squares such as 1369. The number is split into digit pairs from the right, making the calculation manageable. For 1369, the digit pairs become 13 and 69. The first task involves determining a number whose square fits into the first group, 13. The square of 3 yields 9, which is the largest square less than or equal to 13, so 3 becomes the initial digit of the root.
The square of this first digit, 9, is subtracted from 13, leaving a remainder of 4. The next pair, 69, is brought down, forming 469. Now the current quotient, 3, is doubled, resulting in 6, which acts as the base for constructing the next part of the divisor. The goal is to find a digit that, when added to 60 and multiplied by itself, remains within the limit of 469. Trying 7 satisfies this, because (60 + 7) multiplied by 7 gives exactly 469.
Once 469 is subtracted by itself, the result is 0, meaning the process is complete, and no remainder is left. The full quotient now reads 37. Therefore, 37 is the square root of 1369.
This method not only ensures accuracy but also builds number sense, helping to develop confidence in solving roots manually. It serves as a foundation for understanding roots without relying solely on calculators, particularly useful during examinations or mental math exercises.
