Using a number line what whole number and rational number to the nearest half is √105 between?
A. Between 10.5 and 11
B. Between 11 and 11.5
C. Between 9.5 and 10
D. Between 10 and 10.5
To determine which whole number and rational number to the nearest half is √105 between, we need to find the whole numbers that are closest to √105.
The square root of 105 is approximately equal to 10.246.
Between the whole numbers 10 and 11, which are the closest to √105, the nearest half is 10.5.
Therefore, √105 is between 10 and 10.5.
Therefore, the correct answer is D. Between 10 and 10.5.
To determine the whole number and rational number closest to √105, we can find the whole numbers around √105 on the number line.
First, let's determine the whole numbers that √105 is between:
√105 ≈ 10.247
Therefore, √105 is between 10 and 11.
Next, let's find the rational number closest to √105 to the nearest half. We can achieve this by looking at the halfway point between 10 and 11:
10 + 0.5 = 10.5
So, √105 is between 10 and 10.5 on the number line.
Therefore, the correct answer is option D. Between 10 and 10.5.