Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 7 and 7.5
between 7.5 and 8
between 8 and 8.5
between 8.5 and 9
To determine which whole number and rational number to the nearest half is 58−−√, we can use a number line.
The square root of 58 is approximately 7.62. To the nearest half, this would be 7.5.
Therefore, 58−−√ is between the whole number 7 and the rational number 7.5.
The correct response is "between 7 and 7.5."
To find the whole number and rational number closest to √58, we can first calculate the value of √58. Using a calculator, we find that √58 is approximately 7.615.
Now, to determine the whole number and rational number closest to √58 to the nearest half, we look for the numbers on the number line that are one-half away from 7.615.
Looking at the options provided:
- Between 7 and 7.5: This is not a valid choice because 7.615 is larger than both 7 and 7.5.
- Between 7.5 and 8: This is the correct choice because 7.615 is closer to 7.5 than it is to 8.
- Between 8 and 8.5: This is not a valid choice because 7.615 is smaller than both 8 and 8.5.
- Between 8.5 and 9: This is not a valid choice because 7.615 is smaller than both 8.5 and 9.
Therefore, the whole number and rational number closest to √58 to the nearest half is between 7.5 and 8.