Using a number line, we can find the nearest whole number and rational number to the nearest half that 10−−√ is between.
To do this, let's first find the square root of 10, which is approximately 3.162.
The nearest whole number to 3.162 is 3.
To find the nearest half, we need to consider the number line from 3 to 4, divided into halves. The midpoint between 3 and 4 is 3.5.
Since 10−−√ is greater than 3.5, the nearest whole number and rational number to the nearest half that 10−−√ is between are 4 and 3.5, respectively.
Therefore, 10−−√ is between 4 and 3.5 on the number line.