Question

Which of the following rational numbers is not between 3–√ and 6–√ ?

Show your work.

(1 point)
Responses

1.81 point 8

4–√square root of 4

1.51 point 5

22

Answer 1

To determine which rational number is not between \( \sqrt{3} \) and \( \sqrt{6} \), we first need to find the approximate decimal 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 identify the range:
- The interval we are considering is approximately \( 1.732 < x < 2.449 \).

Next, we evaluate the given options:

1. **Option 1: 1.8**
- \( 1.732 < 1.8 < 2.449 \) — This number is between \( \sqrt{3} \) and \( \sqrt{6} \).

2. **Option 2: \( \sqrt{4} \)**:
- \( \sqrt{4} = 2 \)
- \( 1.732 < 2 < 2.449 \) — This number is between \( \sqrt{3} \) and \( \sqrt{6} \).

3. **Option 3: 1.5**
- \( 1.5 < 1.732 \) — This number is **not** between \( \sqrt{3} \) and \( \sqrt{6} \).

4. **Option 4: 22**
- \( 22 > 2.449 \) — This number is also **not** between \( \sqrt{3} \) and \( \sqrt{6} \).

Now we summarize our findings:
- Values in between: \( 1.8 \) and \( \sqrt{4} = 2 \)
- Values not in between: \( 1.5 \) and \( 22 \)

However, the question specifically asks for a rational number that is **not** between \( \sqrt{3} \) and \( \sqrt{6} \).

Thus, the rational number that is not between \( \sqrt{3} \) and \( \sqrt{6} \) is:
**1.5**.