To find the square root of \(625\) using the division method (also known as the long division method), follow these steps:

### Step-by-Step Solution:

1. **Pair the Digits from Right to Left**:  
   Start by pairing the digits of the number 625 from right to left. Here, the number \(625\) can be paired as \(6\) and \(25\).

2. **Find the Largest Integer**:  
   Find the largest integer whose square is less than or equal to the leftmost pair or single digit. In this case, the leftmost part is \(6\).

   - The largest integer whose square is less than or equal to \(6\) is \(2\) (since \(2^2 = 4\) and \(3^2 = 9\) which is greater than \(6\)).

3. **Subtract and Bring Down Next Pair**:  
   - Subtract \(4\) (which is \(2^2\)) from \(6\), which gives \(2\).  
   - Bring down the next pair of digits (which is \(25\)), making the number \(225\).

4. **Find the Next Digit of the Root**:  
   - Double the current quotient (which is \(2\)) to get \(4\).
   - Now find a digit \(X\) such that \(4X \times X \leq 225\).

   - The suitable \(X\) is \(5\) because:
     \[
     45 \times 5 = 225
     \]
     This exactly matches \(225\).

5. **Subtract and Continue**:  
   - Subtract \(225\) from \(225\), which gives \(0\).

Since there are no more pairs to bring down and the remainder is \(0\), the square root calculation is complete.

### Result:
The square root of \(625\) is **25**.

Would you like to go through any of the steps in more detail, or do you have any questions?

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### Expanded Questions:

1. How would you find the square root of a number that is not a perfect square using the division method?
2. What is the process to find the cube root of a number using a similar division method?
3. How can you find the square root of a decimal number using the division method?
4. How does the division method for square roots compare to the estimation method?
5. Why does the division method work for finding square roots?

### Tip:
When using the division method to find square roots, make sure to carefully align your digits and work through each step methodically to avoid mistakes.

Learn how to find the square root of 625 using the division method. Step-by-step solution with detailed instructions on pairing digits, finding integers, and subtracting. Suitable for Grades 7-9 students learning mathematical methods.

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