To approximate the value of \( \sqrt{39} \) on a number line, we can identify the perfect squares closest to 39. The squares of 6 and 7 are:
- \( 6^2 = 36 \)
- \( 7^2 = 49 \)
This means \( \sqrt{39} \) lies between 6 and 7. To narrow it down further, we check more decimal values:
- \( 6.1^2 = 36.61 \) (too low)
- \( 6.2^2 = 38.44 \) (still too low)
- \( 6.3^2 = 39.69 \) (too high)
Now we know that \( \sqrt{39} \) is between \( 6.2 \) and \( 6.3 \). To get even closer, we can check:
- \( 6.25^2 = 39.0625 \) (too high)
- \( 6.24^2 = 38.2976 \) (too low)
From this information, we see that \( \sqrt{39} \) is between \( 6.24 \) and \( 6.25 \), so the approximate value to choose from your options is closer to \( 6.25 \).
Therefore, the answer is \( 6.25 \).
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