The square root of 1238578 is :

Options

A. 3254
B. 3724
C. 3258
D. None of these

Answer

To find the square root of the number 1238578, we will follow a systematic approach to determine whether it is a perfect square or not.

### Step-by-Step Solution:

1. **Check if the number is a perfect square**:
- A perfect square is a number that can be expressed as the square of an integer. To determine if 1238578 is a perfect square, we can use two rules based on the properties of perfect squares.

2. **Calculate the digital sum**:
- The digital sum is obtained by adding all the digits of the number together.
- For 1238578, we calculate:
- 1 + 2 + 3 + 8 + 5 + 7 + 8 = 34
- Now, we further add the digits of 34: 3 + 4 = 7
- The digital sum of 1238578 is 7.

3. **Check the digital sum against perfect square rules**:
- The digital sum of a perfect square can only be 1, 4, 7, or 9. Since our digital sum is 7, this condition is satisfied.

4. **Check the unit digit**:
- The unit digit of 1238578 is 8.
- According to the rules, a perfect square cannot have a unit digit of 2, 3, 7, or 8. Since the unit digit is 8, this indicates that 1238578 is not a perfect square.

5. **Conclusion**:
- Since 1238578 fails the second condition (the unit digit is 8), we conclude that it is not a perfect square. Therefore, the square root of 1238578 is not a rational number and cannot be expressed as an integer.

### Final Answer:
The square root of 1238578 is not a perfect square, and thus it is irrational.

---