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

Answer 1

To find where \( \sqrt{58} \) lies on a number line, we first approximate \( \sqrt{58} \).

We know that:

• \( 7^2 = 49 \)
• \( 8^2 = 64 \)

Since \( 49 < 58 < 64 \), it follows that: \[ 7 < \sqrt{58} < 8 \]

Next, we can narrow it down further by calculating \( \sqrt{58} \) approximately: \[ \sqrt{58} \approx 7.6158 \]

Now, we need to identify the nearest half. The number \( 7.6158 \) is between \( 7.5 \) and \( 8 \).

Thus, \( \sqrt{58} \) is between the rational number \( 7.5 \) and the whole number \( 8 \).

Therefore, the answer is: between 7.5 and 8.