Question

Which of the following rational numbers is not between 3–√ and 6–√ ? Show your work. (1 point) Responses 1.8 1 point 8 4–√ square root of 4 1.5 1 point 5 2

Answer 1

To determine which of the provided rational numbers is not between \(\sqrt{3}\) and \(\sqrt{6}\), we first need to calculate the approximate values of \(\sqrt{3}\) and \(\sqrt{6}\).

1. **Calculate \(\sqrt{3}\)**:
\[
\sqrt{3} \approx 1.732
\]

2. **Calculate \(\sqrt{6}\)**:
\[
\sqrt{6} \approx 2.449
\]

Now we can see that the interval between \(\sqrt{3}\) and \(\sqrt{6}\) is approximately \( [1.732, 2.449] \).

Next, let’s check the provided rational numbers to determine which one does not lie within this range:

1. **1.8**:
\[
1.8 \text{ is between } 1.732 \text{ and } 2.449.
\]

2. **8**:
\[
8 \text{ is not between } 1.732 \text{ and } 2.449.
\]

3. **\(\sqrt{4}\)**:
\[
\sqrt{4} = 2 \text{ is between } 1.732 \text{ and } 2.449.
\]

4. **1.5**:
\[
1.5 \text{ is not between } 1.732 \text{ and } 2.449.
\]

5. **5**:
\[
5 \text{ is not between } 1.732 \text{ and } 2.449.
\]

6. **2**:
\[
2 \text{ is between } 1.732 \text{ and } 2.449.
\]

From the options above, the numbers that do not lie between \(\sqrt{3}\) and \(\sqrt{6}\) are **8** and **1.5**. However, in the context of your question about which of the numbers provided, it is clear that "8" is the most substantially outside the range.

Thus, the answer is:

**8 is not between \(\sqrt{3}\) and \(\sqrt{6}\).**