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

Question

Responses

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

6–√<2
6–√<2

0<4–√
0<4–√

8–√<5
8–√<5

8–√>6–√

Answer 1

Let's evaluate each inequality one by one.

1. 8–√ > 3: This means \(\sqrt{8} > 3\). Since \(\sqrt{8} \approx 2.83\), this inequality is false.

2. 6–√ < 2: This means \(\sqrt{6} < 2\). Since \(\sqrt{6} \approx 2.45\), this inequality is false.

3. 0 < 4–√: This means \(0 < \sqrt{4}\). Since \(\sqrt{4} = 2\), this inequality is true.

4. 8–√ < 5: This means \(\sqrt{8} < 5\). Since \(\sqrt{8} \approx 2.83\), this inequality is true.

5. 8–√ > 6–√: This means \(\sqrt{8} > \sqrt{6}\). Since \(\sqrt{8} \approx 2.83\) and \(\sqrt{6} \approx 2.45\), this inequality is true.

So the three correct answers are:

• \(0 < 4–√\)
• \(8–√ < 5\)
• \(8–√ > 6–√\)