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📝 Finding Square Root by Division Method (Step by Step)

The division method is a simple way to find the square root of large numbers without a calculator. Let’s learn the steps with an example.

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🔹 Steps of the Division Method

1. Group the digits of the number in pairs from right to left.

2. Find the largest square smaller than or equal to the first group.

3. Subtract and bring down the next group of digits.

4. Double the quotient (answer so far) → this becomes the starting divisor.

5. Find a digit that works with this divisor to fit into the new dividend.

6. Repeat until all pairs are used.

7. The result is the square root.

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🔹 Example: Find √784

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Step 1: Group the digits

We write 784 as:

7 | 84

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Step 2: Largest square less than 7

2 × 2 = 4   (fits)  
3 × 3 = 9   (too big)  

So, the first digit is 2.

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Step 3: Subtract and bring down next pair

   2
  ------
√784 | 7 | 84
     -4
     ----
      3 → bring down 84 → 384

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Step 4: Double the quotient

2 × 2 = 4

So, the new divisor will start with 4_.

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Step 5: Find the next digit

We need a digit (let’s call it x) such that:

(40 + x) × x ≤ 384

Trying 8:

48 × 8 = 384 ✅

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Step 6: Subtract

   28
  ------
√784 | 7 | 84
     -4
     ----
      384
     -384
     -----
        0

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✅ Final Answer

√784 = 28

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🔹 Conclusion

The square root of 784 is 28.
This method works for any large perfect square (and can also be extended for non-perfect squares to find decimal values).