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

Question

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. \( \sqrt{8} < 5 \)