Question

Using a number line, what whole number and rational number to the nearest half is 68−−√%0D%0A68%0D%0A between?%0D%0A%0D%0AShow your work. %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0Abetween 8 and 8.5%0D%0Abetween 8 and 8.5%0D%0A%0D%0Abetween 8.5 and 9%0D%0Abetween 8.5 and 9%0D%0A%0D%0Abetween 9 and 9.5%0D%0Abetween 9 and 9.5%0D%0A%0D%0Abetween 7.5 and 8

Answer 1

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Answer 2

To determine the whole number and the nearest half that \( \sqrt{68} \) is between, we first need to calculate \( \sqrt{68} \).

1. **Calculate \( \sqrt{68} \)**:
\[
\sqrt{68} = \sqrt{4 \times 17} = 2 \sqrt{17}
\]
Since \( \sqrt{17} \) is not a whole number, we can find its approximate value using a calculator.

Using the calculator:
\[
\sqrt{17} \approx 4.123
\]
Thus,
\[
\sqrt{68} \approx 2 \times 4.123 \approx 8.246
\]

2. **Determine the whole number and rational number to the nearest half**:
- The whole number that \( 8.246 \) is between is 8 and 9.
- To find the nearest half, we check:
- \( 8.246 \) is closer to 8.5 than to 8.
- Thus, \( \sqrt{68} \) is between \( 8.2 \) and \( 8.5 \).

3. **Conclusion**:
Therefore, \( \sqrt{68} \) is approximately between:
- Between **8 and 8.5**.

Final answer:
**Between 8 and 8.5.**

Answer 3

To find the range for \( \sqrt{68} \):

1. Calculate \( \sqrt{68} \):
\[
\sqrt{68} \approx 8.246
\]

2. Determine the interval:
- Whole numbers: 8 and 9
- Nearest half: Closer to 8.5

Therefore, \( \sqrt{68} \) is between **8 and 8.5**.