Find square root of 15.25 by division method upto 3 decimal
The Correct Answer and Explanation is:
Correct Answer:
The square root of 15.25 using the long division method up to three decimal places is:
√15.25 ≈ 3.905
🔍 Step-by-Step Explanation (Long Division Method):
- Pair the Digits:
Start by placing the number in pairs from the decimal point.- 15.25 → Pair as: (15)(25)
- Find Initial Root:
- Find the largest number whose square is ≤ 15.
- 3² = 9 and 4² = 16 → So choose 3.
- Write 3 as the first digit of the square root.
- Subtract 9 from 15:
15 − 9 = 6 - Bring down next pair (25): Now we have 625.
- Double the Quotient:
- Double of 3 = 6. Write it as a divisor prefix.
- Try numbers like 61×1 = 61, 62×2 = 124, …, 69×9 = 621
- 69×9 = 621 ≤ 625
- Choose 9
- Write 9 as the next digit after decimal: 3.9
- Subtract 621 from 625 → remainder = 4
- Bring down next pair (00): Now you have 400
- Repeat the Process:
- Double 39 = 78. Use 78_ as divisor.
- Try 781×1 = 781, 782×2 = 1564, …, 785×5 = 3925
- 785×5 = 3925 ≤ 4000
- Choose 5
- Write 5: √15.25 = 3.905
- Subtract 3925 from 4000 = 75
- Bring down next pair (00): Now 7500
- Continue:
- Double 3905 = 7810
- Try 78101×1 = 78101, too big.
- 7801×1 = 7801, too big → Try 780×0 = 0
- We stop at 3 decimal places: √15.25 ≈ 3.905
📘 Conclusion:
The square root of 15.25 using the long division method up to three decimal places is 3.905. This method breaks down square roots step-by-step, ensuring precise manual calculation without a calculator. It’s especially helpful in exams or competitive tests where calculators are not allowed.