Question

Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)

Answer 1

To find the whole number and the rational number to the nearest half that \( \sqrt{58} \) is between, we first need to calculate \( \sqrt{58} \).

Calculating:
\[
\sqrt{58} \approx 7.61577
\]

Next, we identify the whole number that \( \sqrt{58} \) is between. The nearest whole numbers are 7 and 8:

\[
7 < \sqrt{58} < 8
\]

Now, to determine the rational number to the nearest half, we check the nearest half values around \( 7.61577 \), which are \( 7.5 \) and \( 8.0 \). Since \( 7.61577 \) is closer to \( 7.5 \) than \( 8.0 \):

Thus, we can conclude:
- \( \sqrt{58} \) is between the whole numbers **7** and **8**.
- \( \sqrt{58} \) is closest to the rational number **7.5** (to the nearest half).

In summary:
- Whole numbers: 7 and 8
- Rational number to the nearest half: 7.5