Question

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

8–√>3
square root of 8 is greater than 3

0<4–√
0<4–√

8–√>6–√
square root of 8 is greater than square root of 6

8–√<5
8–√<5

6–√<2
6–√<2

Answer 1

Let's evaluate each of the inequalities:

1. **\( \sqrt{8} > 3 \)**
\(\sqrt{8} \approx 2.83\), which is **not greater than 3**.
**False**

2. **\( 0 < 4 - \sqrt{4} \)**
\(\sqrt{4} = 2\), so \(4 - \sqrt{4} = 4 - 2 = 2\).
\(0 < 2\) is **True**.
**True**

3. **\( \sqrt{8} > \sqrt{6} \)**
\(\sqrt{8} \approx 2.83\) and \(\sqrt{6} \approx 2.45\).
Since \(2.83 > 2.45\), this is **True**.
**True**

4. **\( \sqrt{8} < 5 \)**
\(\sqrt{8} \approx 2.83\), and \(2.83 < 5\) is **True**.
**True**

5. **\( \sqrt{6} < 2 \)**
\(\sqrt{6} \approx 2.45\), which is **not less than 2**.
**False**

The correct inequalities are:
- \( 0 < 4 - \sqrt{4} \)
- \( \sqrt{8} > \sqrt{6} \)
- \( \sqrt{8} < 5 \)

Thus, the three true inequalities are:

1. **\( 0 < 4 - \sqrt{4} \)**
2. **\( \sqrt{8} > \sqrt{6} \)**
3. **\( \sqrt{8} < 5 \)**