What is the square root up to two decimal places by long division of 261
What is the square root up to two decimal places by long division of 261
The Correct Answer and Explanation is:
✅ Square Root of 261 by Long Division Method (Up to Two Decimal Places):
The square root of 261 up to two decimal places is:16.15\boxed{16.15}16.15
📘 Step-by-Step Explanation Using the Long Division Method:
The long division method is a manual technique to find the square root of a number. Let’s go through the steps to find the square root of 261 up to two decimal places.
🔹 Step 1: Pair the digits
We group the number 261 into pairs from right to left:
- 2 | 61
- To go beyond the decimal, add pairs of 00: 2 | 61 | 00 | 00
🔹 Step 2: Find the largest square less than or equal to the first group
- First group is 2.
- The largest square less than 2 is 1 (1²), so we put 1 as the divisor and quotient.
- Subtract: 2 – 1 = 1
- Bring down the next pair (61): New dividend is 161
- Double the quotient (1 × 2 = 2), and place as the start of the new divisor.
🔹 Step 3: Find next digit (X)
We try 23 × 3 = 69 → too small
Try 26 × 6 = 156 ✅
- Subtract: 161 – 156 = 5
- Quotient becomes 16
🔹 Step 4: Bring down next pair (00): New dividend = 500
- Double quotient: 16 × 2 = 32
- Try 321 × 1 = 321 ✅
- Subtract: 500 – 321 = 179
🔹 Step 5: Bring down next pair (00): New dividend = 17900
- New divisor base: 161 × 2 = 32
- Try 325 × 5 = 1625
… Eventually we get 16.15 after trying several digits.
🎯 Final Answer:
261≈16.15\sqrt{261} \approx \boxed{16.15}261≈16.15
📘 Conclusion:
The long division method gives a reliable manual process to find the square root of a number. Although calculators are faster, this method helps strengthen understanding of number operations and is especially useful where electronic devices are not allowed (such as exams). The answer, 16.15, is accurate up to two decimal places.
