find square root of 15.25 by division method upto 3 decimal

The Correct Answer and Explanation is:

√15.25 by Division Method (up to 3 decimal places)

We will now find the square root of 15.25 using the long division method, step-by-step.

✅ Answer:

√15.25 ≈ 3.905 (correct to 3 decimal places)

📘 Explanation

The long division method is a traditional technique used to find square roots of numbers (especially non-perfect squares) up to a desired number of decimal places. It is particularly useful when calculators are not allowed, such as in exams.

Here is how we find √15.25 step by step:

1. Group the Digits:

Write 15.25 as 15.25 00 00 (adding pairs of zeros for decimal places).
Group digits in pairs from the decimal point: 15 | 25 | 00 | 00

2. Find the Largest Square ≤ First Group (15):

3² = 9 and 4² = 16 → use 3
Put 3 as the first digit of the root.
Subtract 9 from 15 → remainder = 6
Bring down next pair → new dividend = 625

3. Double the root (3 → 6), find next digit (D):

Try (60 + D) × D ≤ 625
Try D = 9: (60 + 9) × 9 = 69 × 9 = 621
It’s valid → next digit is 9
Root so far = 3.9
Subtract: 625 – 621 = 4
Bring down next pair → 400

4. Double root (3.9 → 78), find next digit:

Try (780 + D) × D ≤ 400
Try D = 0 → 780 × 0 = 0 → fits
Next digit = 0 → Root = 3.90
Subtract: 400 – 0 = 400
Bring down next pair → 40000

5. Double root (3.90 → 780), find D:

Try D = 5: (7800 + 5) × 5 = 7805 × 5 = 39025
Fits → next digit is 5
Final root = 3.905

Hence, √15.25 ≈ 3.905 (correct up to 3 decimal places).