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

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–√

1 answer

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:

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