Question

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

Show your work.

(1 point)
Responses

1.8

√4
square root of 4

1.5

2

Answer 1

To determine which of the given rational numbers 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 \( \sqrt{6} \)**:
\[
\sqrt{6} \approx 2.449
\]

Thus, the range we are considering is approximately between \( 1.732 \) and \( 2.449 \).

Now, we will evaluate each of the given numbers to see if they fall within this range:

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

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

3. **1.5**:
\[
1.5 \text{ is less than } 1.732
\]

4. **2**:
\[
2 \text{ is between } 1.732 \text{ and } 2.449
\]

From this analysis, we can see that:

- \( 1.8 \), \( \sqrt{4} \), and \( 2 \) are all between \( \sqrt{3} \) and \( \sqrt{6} \).
- \( 1.5 \) is less than \( \sqrt{3} \), and therefore is **not between \( \sqrt{3} \) and \( \sqrt{6} \)**.

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