To estimate the value of \( \sqrt{39} \), we can consider the perfect squares around 39:
- \( 6^2 = 36 \)
- \( 7^2 = 49 \)
This means that \( \sqrt{39} \) is between 6 and 7.
To narrow it down further:
- \( 6.2^2 = 38.44 \)
- \( 6.3^2 = 39.69 \)
So, \( \sqrt{39} \) is between 6.2 and 6.3. Since the square of 6.2 is less than 39 and the square of 6.3 is more than 39, the approximate value of \( \sqrt{39} \) is closer to 6.25.
Now, we can check \( 6.25^2 \):
- \( 6.25^2 = 39.0625 \), which is slightly above 39.
Therefore, the approximate value of \( \sqrt{39} \) is around 6.25.
So the answer is: 6.25