Using a number line, what whole number and rational number to the nearest half is √105 between?(1 point)
Responses
A. between 11 and 11.5
B. between 9.5 and 10
C. between 10.5 and 11
D. between 10 and 10.5
To determine the whole number and rational number to the nearest half that √105 is between, we can first find the actual value of √105. Taking the square root of 105, we find that √105 is approximately 10.246.
Now, let's use a number line to determine the whole number and rational number to the nearest half that √105 is between:
|-----|-----|-----|-----|-----|-----|
9 9.5 10 10.5 11 11.5 12
Since √105 is closer to 10 than it is to 11, the whole number is 10. Next, we need to determine the rational number to the nearest half between 10 and 11.
10 < √105 < 11
To find the midpoint between 10 and 11, we add them together and divide by 2:
(10 + 11)/2 = 21/2 = 10.5
So, the whole number and rational number to the nearest half that √105 is between is 10 and 10.5.
Therefore, the answer is D. between 10 and 10.5.