To find the position of \( \sqrt{58} \) on a number line, we first need to determine its approximate value.
Calculating \( \sqrt{58} \):
Since \( 7^2 = 49 \) and \( 8^2 = 64 \), we know that \( \sqrt{58} \) is between 7 and 8.
Now we can check where it is more precisely. We can calculate as follows:
- \( 7.5^2 = 56.25 \) (too low)
- \( 7.6^2 = 57.76 \) (still too low)
- \( 7.7^2 = 59.29 \) (too high)
So, \( \sqrt{58} \) is between \( 7.6 \) and \( 7.7 \).
Since we are asked to provide a response in whole number and rational number to the nearest half, we find:
- The whole number is 7.
- The rational number to the nearest half is 7.5 (since \( 7.6 \) falls between \( 7.5 \) and \( 8 \)).
Therefore, the answer is:
between 7.5 and 8.
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