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Using a number line, what whole number and rational number to the nearest half is [tex]\sqrt{10}[/tex] between? (1 point)

[tex]\sqrt{10}[/tex] is between [tex]\square[/tex] and [tex]\square[/tex].

Sagot :

GinnyAnsweridn
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.
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