Question
What whole number and rational number to the nearest half is the square root of 10 between?
Answers
GPT-4o mini
To find the whole number and rational number to the nearest half that the square root of 10 lies between, we first calculate the approximate value of \(\sqrt{10}\).
Calculating gives:
\[
\sqrt{10} \approx 3.162
\]
Now, we can determine the whole numbers and the nearest half:
1. The whole number before 3.162 is 3, and the whole number after is 4. So, \(\sqrt{10}\) lies between the whole numbers 3 and 4.
2. For the nearest half, we consider the values of 3 and 4 again:
- The halfway point between 3 and 4 is \(3.5\).
- Since \(3.162\) is closer to 3 than to 3.5, the nearest half is 3.5.
Thus, the square root of 10 lies between the whole number **3** and the rational number to the nearest half **3.5**.
Calculating gives:
\[
\sqrt{10} \approx 3.162
\]
Now, we can determine the whole numbers and the nearest half:
1. The whole number before 3.162 is 3, and the whole number after is 4. So, \(\sqrt{10}\) lies between the whole numbers 3 and 4.
2. For the nearest half, we consider the values of 3 and 4 again:
- The halfway point between 3 and 4 is \(3.5\).
- Since \(3.162\) is closer to 3 than to 3.5, the nearest half is 3.5.
Thus, the square root of 10 lies between the whole number **3** and the rational number to the nearest half **3.5**.