Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Responses
between 11 and 11.5
between 10 and 10.5
between 9.5 and 10
between 10.5 and 11
To find the whole number and rational number to the nearest half that 105−−−√ is between, we can use a number line.
First, find the whole number that is closest to the square root of 105. The square root of 105 is approximately 10.24. The whole number closest to 10.24 is 10.
Next, find the nearest half between 10 and 11. This would be 10.5.
Therefore, 105−−−√ is between 10 and 10.5.
So the correct answer is:
between 10 and 10.5.
To determine the whole number and rational number to the nearest half that is between √105 on a number line, we can approximate the value of √105.
Using a calculator, we find that √105 is approximately 10.247.
To find the whole number and rational number to the nearest half, we look for the closest integers to this value.
10 is the closest whole number, and 10.5 is the nearest half.
Therefore, the whole number and rational number to the nearest half that is between √105 on a number line is between 10 and 10.5. Hence, the correct response is:
between 10 and 10.5