Question

Which inequalities are true? Select the three correct answers.(3 points)
Responses

8–√>2
square root of 8 is greater than 2

9–√<12−−√
9–√<12−−√

8–√>8
square root of 8 is greater than 8

0<5–√
0<5–√

6–√<2–√

Answer 1

To assess the inequalities given, let's evaluate each one:

1. **\( \sqrt{8} > 2 \)**
- \( \sqrt{8} \) is approximately \( 2.828 \), which is greater than \( 2 \).
- This inequality is **true**.

2. **\( \sqrt{9} < \sqrt{12} \)**
- \( \sqrt{9} = 3 \) and \( \sqrt{12} \) is approximately \( 3.464 \), so \( 3 < 3.464 \).
- This inequality is **true**.

3. **\( \sqrt{8} > 8 \)**
- \( \sqrt{8} \) is approximately \( 2.828 \), which is not greater than \( 8 \).
- This inequality is **false**.

4. **\( 0 < \sqrt{5} \)**
- \( \sqrt{5} \) is approximately \( 2.236 \), which is indeed greater than \( 0 \).
- This inequality is **true**.

5. **\( \sqrt{6} < \sqrt{2} \)**
- \( \sqrt{6} \) is approximately \( 2.449 \) and \( \sqrt{2} \) is approximately \( 1.414 \), so \( 2.449 > 1.414 \).
- This inequality is **false**.

Therefore, the three correct inequalities that are true are:

1. **\( \sqrt{8} > 2 \)**
2. **\( \sqrt{9} < \sqrt{12} \)**
3. **\( 0 < \sqrt{5} \)**