Question

Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)Responsesbetween 7 and 7.5between 7 and 7.5between 7.5 and 8between 7.5 and 8between 8 and 8.5between 8 and 8.5between 8.5 and 9between 8.5 and 9

Answer 1

To determine where \(\sqrt{58}\) falls on a number line, we can calculate its approximate value.

To find \(\sqrt{58}\):
- We know that \(7^2 = 49\) and \(8^2 = 64\).
- This means that \(7 < \sqrt{58} < 8\).

Now, to find a more precise value, we can calculate the decimal value:
\[
\sqrt{58} \approx 7.615
\]

Next, we can see which half-interval \(\sqrt{58}\) falls into:
- Between \(7.5\) and \(8\) is \([7.5, 8)\).
- Since \(7.615\) is greater than \(7.5\) but less than \(8\), it lies in this range.

Hence, \(\sqrt{58}\) is between \(7.5\) and \(8\).

So, the answers are:
- Whole number: \(7\)
- Rational number to the nearest half: \(7.5\)

Thus, the correct response is:

**Between 7.5 and 8.**