To determine which range the number \( \sqrt{58} \) falls between, we first calculate \( \sqrt{58} \).
Calculating \( \sqrt{58} \):
- We know that \( 7^2 = 49 \) and \( 8^2 = 64 \).
- This means \( \sqrt{58} \) is between 7 and 8.
Next, we can estimate \( \sqrt{58} \) further:
To find a more precise value, we can approximate:
Since \( 7.5^2 = 56.25 \) and \( 8^2 = 64 \), this shows:
- \( 7.5^2 < 58 < 8^2 \)
- Therefore, \( \sqrt{58} \) is between 7.5 and 8.
Now let's identify the rational number to the nearest half.
Since \( 7.5 < \sqrt{58} < 8 \), it rounds to 7.5 when considering to the nearest half.
Thus, the whole number is 7, and the rational number to the nearest half is 7.5.
So the final answer is:
between 7.5 and 8.