Find the square root of 18769.

Answer

To find the square root of 18769, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Last Two Digits**:
- The last two digits of 18769 are 69.

2. **Determine Possible Units Digits**:
- The unit digit of the square root can either be 3 or 7 because:
- \(3^2 = 9\) (last digit is 9)
- \(7^2 = 49\) (last digit is 9)

3. **Estimate the Range for the Square Root**:
- We need to find a perfect square close to 18769. The nearest perfect squares are:
- \(137^2 = 18769\)
- \(138^2 = 19044\)
- Since \(137^2\) is less than \(18769\) and \(138^2\) is greater, we can conclude that the square root of 18769 is around 137.

4. **Calculate the Square**:
- To confirm, we can calculate \(137^2\):
\[ 137 \times 137 = 18769 \]

5. **Conclusion**:
- Therefore, the square root of 18769 is \(137\).

### Final Answer:
The square root of 18769 is \(137\).