Find the square root of 3600.

Answer

To find the square root of 3600 using the long division method, follow these steps:

### Step 1: Pair the digits
Start by pairing the digits of the number 3600 from right to left. We can pair them as follows:
- 36 | 00

### Step 2: Find the largest square
Now, look at the first pair (36). We need to find the largest integer whose square is less than or equal to 36. The largest integer is 6, since \(6^2 = 36\).

### Step 3: Write down the result
Write down 6 above the line as part of the square root. This means the square root of 3600 starts with 6.

### Step 4: Subtract and bring down the next pair
Subtract \(36\) from \(36\) which gives us \(0\). Now, bring down the next pair (00) next to it, resulting in \(00\).

### Step 5: Double the current result
Double the number we have above the line (which is 6). So, \(2 \times 6 = 12\).

### Step 6: Find the next digit
Now we need to find a digit \(x\) such that \(12x \times x\) is less than or equal to \(00\). The only digit that satisfies this is \(0\) because \(120 \times 0 = 0\).

### Step 7: Write down the next digit
Write down \(0\) next to \(6\) above the line, making it \(60\).

### Step 8: Final result
Since we have no more pairs to bring down, the square root of 3600 is \(60\).

### Final Answer:
The square root of 3600 is **60**.

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