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It looks like you're performing a manual square root calculation for 603 using a grid method, sometimes called the long division method for square roots. Here’s a step-by-step outline of how this method works for √603:

1. **Divide the number into pairs of digits**: Starting from the decimal point, group the digits of 603 into pairs. You have 6 | 03.

2. **Find the largest square number** less than or equal to the first pair (6 in this case):
   - The largest square number less than or equal to 6 is 4 (since \(2^2 = 4\)).
   - Place 2 as the first digit of the square root.

3. **Subtract and bring down the next pair of digits**:
   - Subtract 4 from 6 to get 2.
   - Bring down the next pair of digits (03), so you now have 203.

4. **Double the current quotient (2)**: The double of 2 is 4. This is the first part of your divisor.

5. **Find the next digit**: Find the digit \(x\) such that when you multiply \(4x\) by \(x\), it’s as close as possible to 203.
   - If you try 4, you get \(44 \times 4 = 176\).
   - Subtract 176 from 203 to get 27.

6. **Bring down zeros (if needed)** to continue finding more decimal places for the square root.

At this point, it seems you're already starting the calculation manually. Do you want me to continue the steps to calculate √603 further, or explain another step in more detail?

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**Follow-up questions**:
1. Do you want a more detailed explanation of each step in the long division method for square roots?
2. Would you like to calculate the square root to more decimal places?
3. Are you familiar with other methods for approximating square roots?
4. Do you need to know how to apply this method to other numbers?
5. Would you prefer understanding this process with another example?

**Tip**: The grid method is great for understanding how square roots work manually, but calculators can provide quick approximations if you need fast results.

Learn how to manually calculate the square root of 603 using the long division method. This problem covers key mathematical concepts, including square roots and long division, making it ideal for students in Grades 7-10.

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