Question

Using a number line, what whole number and rational number to the nearest half is √105 between?
A. Between 9.5 and 10
B. Between 10.5 and 11
C. between 10 and 10.5
D. between 11 and 11.5

Answer 1

how did you get √105 s between 10 and 11 but come up with 11 and 11.5?

Answer 2

First, we need to find the whole number that √105 is between. The approximate value of √105 is 10.25.

Next, we need to find the nearest half to 10.25. The nearest half is 10 because 10 is closer to 10.25 than 10.5 or any other half.

So, √105 is between the whole numbers 10 and 11.

Therefore, the whole number and rational number to the nearest half that √105 is between is D. between 11 and 11.5.

Answer 3

Apologies for the confusion in my previous response. To clarify:

√105 is between 10 and 11 on the number line.

To find the rational number to the nearest half, we need to determine whether √105 is closer to 10 or 11.

To determine this, we can calculate the midpoints between 10 and 10.5, and between 10.5 and 11:

10 + 10.25 = 20.25 / 2 = 10.125
10.5 + 11 = 21.5 / 2 = 10.75

Since the value of √105 is closer to 10.125 than to 10.75, the rational number to the nearest half for √105 is between 10 and 10.5.

Therefore, the correct answer is C. between 10 and 10.5.