To determine the whole number and rational number to the nearest half that √105 is between, we first need to find the closest whole number and rational number to √105.
To find the whole number, we can estimate the square root of 105. The closest whole number would be the square root of 100, which is 10.
To find the rational number to the nearest half, we need to determine if √105 is closer to 10 or 11. We can square both numbers to compare:
10 squared = 100
11 squared = 121
Since 105 is closer to 100 than 121, √105 is closer to 10.
Therefore, √105 is between the whole number 10 and the rational number 10.5 on a number line.