To determine the whole numbers and the nearest rational number to the nearest half that [tex]$\sqrt{10}$[/tex] is between, follow these steps:
1. Identify the two whole numbers surrounding [tex]$\sqrt{10}$[/tex]:
- [tex]$\sqrt{10}$[/tex] is approximately 3.162.
- The whole number just below [tex]$\sqrt{10}$[/tex] is 3.
- The whole number just above [tex]$\sqrt{10}$[/tex] is 4.
Therefore, [tex]$\sqrt{10}$[/tex] lies between the two whole numbers 3 and 4.
2. Find the rational number to the nearest half between these whole numbers and closest to [tex]$\sqrt{10}$[/tex]:
- Consider the half values between the whole numbers 3 and 4, which would be 3.5.
- Since 3.5 is the only half value between 3 and 4, we compare its proximity to [tex]$\sqrt{10}$[/tex].
- Given that [tex]$\sqrt{10}$[/tex] is approximately 3.162, the distance to 3.5 (specifically [tex]$3.5 - \sqrt{10}$[/tex]) is closer than to 3 or 4.
Therefore, [tex]$\sqrt{10}$[/tex] is between the whole numbers 3 and 4, and the nearest rational number to the half is 3.5.
So, [tex]$\sqrt{10}$[/tex] is between 3 and 4.
